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Ice is just water. Water helps with staying hydrated, but carries no nutrients.

Dirty ice sometimes can be contaminated by algae and other things. They could supply some nutrients, but being a small percentage of the ice, the underlying ice needs to be eaten in large amounts. And here comes the second problem: ice is cold, and melting it takes away quite some energy, that has to come from the eater's body. Considering that in the Arctic having a decent protection from cold is vital, eating ice and throwing away that hard-won energy doesn't seem like a smart evolutionary move.

Mind that eating ice is not comparable to diving into the sea, like polar bears, seals and penguins do: in their case they have a good insulation to limit heat dissipation. Swallowing and melting ice in the bowel cannot benefit from it.

TL;DR: no. Unless you were some kind of plant. Possibly a weird alien plant with acid for sap.

Even if you could get energy from water (spoiler alert: you're not going to) you'd still need to consume other things, because you can't make any kind of structural compounds from hydrogen and oxygen alone, unless you're actually made of ice, Do you want ice golems? because that's how you get ice golems. Good luck working out a way to power them.

Anyway, you'll need some sort of carbon supply. Happily on earth, you can get carbon from the air, and combined with energy from the sun you can combine it with water to make useful things. Getting energy from the sun, water from the ground and carbon from the air makes you a plant, rather than a "creature" as such. You'll also still need a source of all those other trace elements required to make photosynthesis work.

Finally you'll have all sorts of problems, as a water-based lifeform, consuming ice. Your temperature will drop, your metabolism will slow or malfunction, and finally you'll freeze unless you've got a good source of energy from elsewhere to keep warm. That's why hardly anything eats snow or ice (though some things can live in it, such as ice worms or ice algae and they do well enough).

If you wanted something weird and exotic, you could consider a non-water based biochemistry, using a solvent with a lower freezing point than water. The only kind that seems likely to work well in an earth-like temperature range is hydrogen fluoride, which requires access to a decent source of fluorine-bearing compounds (tricky) and makes you dangerously corrosive to conventional terrestrial life. Ammonia might also work, though you'd boil above −33°C and I don't think you can get enough sunlight to do useful things with and maintain a body temperature that low. In either case, you could "eat" ice, use a photosynthetic process to produce useful energy storage compounds from water and air, and use them in dark and gloomy periods to keep your metabolism going.

The Black Surface Stingray from Auriga IV is what you are looking for.

Auriga IV is one of those ice planets. Along the equator it has a thin 200 km wide biome with some weird creatures in it. The climate is pretty stable since the planet does not wobble when it spins, and because other factors you can ask climate scientists about. Temperature is between -5 and 0 celsius, most of the time. Snows some, but its not extreme.

One of those creatures is the The Black Stingray, a huge, flat, hairy, 15 meters wide thing that filter feeds on the surface snow with a mouth that is almost as big as the whole body. It moves by pedal locomotary waves, rippling the underside of the body, so slow its boring to watch. But what is cool about the stingray? Its the hottest creature on the planet! Its skin its made of natural Vantablack(the blackest black substance known), absorbing up to 99.96% of visible light. The vantablack and the big surface makes this warm blooded creature possible.

The Stingray huge "wings" exist for capturing energy from the sun and storing fat. The body of the creature is a 1 meter long, 50 cm tall between the wings. The wings cand fold slowly around the body to preserve heat during the rare ocasions when the temperature goes down beyond -5 celsius. Also happens during the hibernation period.

Nutrition comes with the help of other creatures. Most Aurigan creatures live underground, in the soil that is just below the almost always thin layer of snow (43 cm in average). A lot of them are algae growers. They grow this green stuff on the ice, then collect it, dry it and keep it in their holes.

But the Stingray is not a fussy eater. While it ingests mainly culture algae, it also goes for the less nutritious wild algae, cadavers, poop, anything, realy.

I don't know how long this species will survive. This much rare and expensive hairy hide, moving so slow...

It is however the blackest black in existence. My wife loves her Black Stingray Coat :D

Nuclear powered creatures and osmotic balance in hypersaline waters.

The creature actually has a nuclear metabolism using some kind of subcritical isotope concentration, you will need to handwave this part, or ask it as a different question. Your creature uses the ice to dissipate heat, it swallows chunks of calving glacier for trace minerals including the isotopes it needs, but it is also using the ice to dissipate heat, the fresh water it generates is more important, especially as polar oceans are often hyper saline. It prefers ice to sea water for cooling as it has to get rid of all the salt it takes in from the sea water, swallowing chunks of ice has far less salt. This does work better if said creature breaths air but it will work with gills as a sort of compensation mechanism, using fresh water to flush salts.

And just becasue it is too perfect I need to share this image. the iceberg devourer.

I'm going to disagree with the above answers and suggest that it might be possible.

It'd be a fairly unusual metabolism, but you could conceivably have a marine creature live in the Arctic eating mainly ice. Around the edges of Greenland's ice sheet, for example, the habitat contains both solid fresh water (ice) and liquid salt water. If your creature "eats" ice and "breathes" saltwater, it can obtain energy from the collapse of the concentration gradient as they mix in its body.

This creature takes an ice meal, maybe from the bottom of an iceberg, and seals its stomach tightly. Separating its stomach from its lung is a thin impermeable membrane, covered in specialised ion channels and well-supplied with blood. These channels allow Na+ and Cl- ions to pass from the lung into the stomach, but not freely: they are constructed in such a way as to decompose water into hydrogen and oxygen gases, which are carried to the rest of the body by the creature's blood. With hydrogen and oxygen in the bloodstream, the creature's cells absorb these two reactive gases as needed, returning water to the blood as a byproduct of exertion. (You can imagine the ion channels as tiny paddlewheels driving electrical generators used to electrolyse water, and the creature's cells as engines burning hydrogen and oxygen to produce work.) As the ions enter the stomach, they cause the ice to melt via freezing point depresssion and build up, reducing the concentration gradient and slowing the metabolism. Eventually the creature must excrete saltwater from its stomach and take another ice meal.

This is a pretty radical difference from most existing creatures, so it probably diverged a long time ago in evolutionary history - its most recent ancestor in common with humans might be a jellyfish! Conveniently, jellyfish are ectothermic and some live and metabolise in Arctic water, so your creature needn't be warm-blooded and spend the energy cost to heat the ice to its own body temperature.

Now for the bad news: possible is not equal to practical. You can't construct much of a body just of the elements discussed so far (hydrogen, oxygen, sodium, chlorine). Remember that membrane it has with the fancy ion channels? That's going to need some carbon and nitrogen at a minimum, so your creature has to have a means to acquire these. So we have a conundrum - why wouldn't an animal just metabolise the carbon, if it can get enough of it to build itself a body? The cellular machinery for metabolising carbon is well-established, and unless the creature takes it up - and thus grows - very slowly, its carbon diet is almost certainly a richer source of energy than its ice diet. For the same reason, a salinity-gradient metabolism is probably limited to powering something resembling an ice-eating leech, and not a quick-witted or quick-moving one (muscles and brains both consume quite a bit of energy).

Another consideration is that, if you can get the raw materials into the creature's body, it's probably worthwhile to design a better means of transporting energy to the cells. Hydrogen gas is not very soluble in water, so the body is going to have a hard time getting enough to burn. You probably need special blood cells to carry hydrogen, as our blood cells carry oxygen, or a system based on a different reaction altogether whose reagents and products are more soluble.

Ultimately here are some obstacles this design would face, but if you want a slow-growing sedentary marine slug to colonise Arctic shorelines and icebergs, you might just get away with it!

This ectothermic creature filter feeds from the ice for the algae and organic material it contains. Imagine something that is

(1) black, so it absorbs energy from the sun in order to melt the ice and pull out the organic food material from it.

Or (2) have a body temperature below that of the melting point of ice, and instead of melting, physically crushes the ice it ingests and sift out the food particles embedded within. Maybe it physically separates the crystal grains to lick out the algae trapped between them with cilia or something

It could exist for two reasons:

(1) the seawater may contain predators that will see it as an easy meal, so it is forced to occupy the niche on or in the ice instead.

Or (2)the sea ice have underwent some form of eutrophication, and as a result, algae that lives in ice and photosynthesize using the abundant refracted sunlight is very abundant within the ice. Maybe your creature will scrape off only the dirty top layer that had the algae accumulated in it.

Or (3)the creature gets its caloric intake from somewhere other than ice, and only uses ice as a source of fresh water. This is especially true for certain mammals that is not fully adapted to living in salt water, so they require additional water that have to be both fresh and is not available in high enough amounts in its food supply. (Think Eskimos, who burns animal fat to melt ice for fresh water) an animal may do the same. it eats a very fatty, water deficient fish, and uses some of the calories from the fat to melt sea ice to get fresh water, as desalinating sea water will cost far more energy than melting ice.)

Engineer here. Dehumidifiers are portable air conditioners that pump the hot air and the cold air out together. The input is wet, room-temperature air. There is an air-conditioning coil (essentially) that cools the air below its dew point. When this happens, some of the water in the air condenses into liquid water. That water is trapped in a drain. The resulting cold air, with less water, is heated by the hot end of the air-conditioner, back up to approximately room temperature.

Your ice-eating organism could work similarly in that the energy used to melt the ice could be recovered by re-freezing the water. Something something anti-freeze blood, but it would essentially "poop" snow or something similar. But, like others have mentioned, there needs to be something in the ice for the thing to eat. There's no point in shuffling water around.

Nutrition would be a main key factor because the creature would need energy to melt the ice into water to absorb it. So they would need to have some sort of energy intake before the ice.

And that's why polar animals (bears or penguins) don't drink water/eat snow. when you need to eat first why not take the water with that caloric intake?

The problem is energy. Ice is, unsurprisingly, quite cold. In order to get hydration value out of it, you need to pump in enough heat to melt the stuff (a fair chunk) which still leaves it at the same temperature, and then enough heat to warm it up to whatever your body temperature is. That body temperature needs to be adequate for whatever metabolic processes you have going on. Starting int he arctic, where heat is not readily available, that's a lot of heat it's costing you, and a pretty heavy associated energy load... in a land not known for plentiful available food.

"could plausibly exist" is a pretty large net. If one did exist, though, it wouldn't be running on standard metabolic paths. The cost of water gain by this technique would be too high. Any animal that depended on ice melting for water gain would be massively outcompeted by other animals that managed it more efficiently.

It would be easier to drink saltwater and filter it then warm up the mass amounts of ice to get enough water to survive (I'm assuming warm-blooded as it's in the arctic, but maybe it has "antifreeze" in its blood and are cold-blooded). The only reason it would do it is if there were "plankton" in the snow and it is a filter-feeder.