Overall, I like it. It's a nicely conceived, though grim, short-short story, and it's clearly speaking to a certain inconvenient truth of which we're lately all too aware. You have to be careful in balancing between your depiction of an event and a too-thinly veiled morality tale about the evils of global warming--if it comes off as smarmy or preachy, no one's going to want to read it. You're doing well with it, but you could probably pull back from the underlying theme a little without losing anything. Now, a few more technical notes...
The cold, dark water surrounded the swimming bear, as it had from time-to-time throughout his long life. Always he would swim for a while, then eventually he would find ice after having found and eaten a seal or something of the sort. He was not a truly massive polar bear, and so he never found it necessary to find a very big piece of ice to rest on.
The opener seems kind of redundant. I mean, chances are good that a "swimming bear" is going to be surrounded by water, right? You can avoid this problem if you remove "swimming" from the first sentence, and then you'd also eliminate the echo with "swim" in the second sentence. But you still have an echo between "find" and "found," which you should probably avoid. Consider "caught" instead of "found," for example.
That day there was no ice to be seen. That was nothing completely unusual, he had swum for plenty of days at a time before, but that had been when he was young and full of energy. Now as an older bear, he could not afford to take such risks.
A little clunky here, I think, in part because the first two sentences begin with "that." "Full of energy" is something of a cliche, too. Maybe consider something like:
That day there was no ice to be seen, though this wasn't unusual. In his youth he could swim for days at a time. But now, a much older bear, he had no energy for such risks.
continuing...
But he had no choice. He kept swimming for that day, and the next, pausing at times to regain his breath, or to trap a fish that swam too near the surface. Fate, however, granted him far too few of these mercies that were necessary if he was too keep swimming for long. And still there was no ice to be seen.
This paragraph comes across as too heavy IMO, particularly because of the invocation of Fate (I'd get rid of that whole sentence, in fact, because it's essentially redundant). You should probably elminate the first sentence, too, because it makes the passage a little too anthropomorphic. Rather than "He kept swimming for that day," consider "He swam all that day," leading into the rest of your sentence as it is. Also, get rid of "to be seen" in the closing sentence, because it's an unnecessary phrase that bogs down the paragraph. Otherwise, this is an effective passage, and it starts to feel like a fatal turning point...
He was just about to yield to the cold water when he saw a solitary piece of ice on the horizon. With his last reserves of energy, he struck out for his salvation. Although he was moving at a quite sluggish pace, he was satisfied that soon he could find rest. He had a glowing sensation that his tribulations of the past few days had been worthwhile.
Again, you veer into anthropomorphizing here, with "yield," "salvation," "satisfied," and "tribulations." All of these, to me, imply nearly human levels of introspection, and in so doing I think you cheat yourself (and the reader) out of a much more pure and powerful moment. Let the bear be a bear without hanging a bunch of humanisms on him. You could probably strip the whole paragraph down to something like:
At last a patch of ice appeared in the distance.
All the rest is either self-evident from what you've already given us or else an awkwardly Disney-esqe glimpse into the animal's "thoughts." Also, "horizon" in this paragraph echoes with the story's closing sentence.
He came closer and closer to the ice, and finally he was on top of it. It wasn’t as big as it had seemed from afar, but the bear knew that it would have to do. He climbed atop the icy slab, shook the freezing water from his fur, settled down, and was asleep almost immediately.
As written, this paragraph is a little awkward because the bear is "on top of" the ice in one sentence and then "climbs atop the icy slab" in the next. Consider combining this paragraph with the preceding:
At last a patch of ice appeared in the distance, and after many hours he reached it. The slab seemed smaller as he approached, but he climbed onto it, shook the freezing water from his fur, and was quickly asleep.
continuing...
He was still asleep when his piece of ice (which had been a part of a glacier not so long ago), broke in half, sending the old bear into the arctic, watery depths. He continued to slumber as his lungs filled with water and he sunk down, down, down.
I'm not a big fan of parentheses in fiction of this length, because they always seem to come across as an effort to shoehorn a piece of information into the text. Because you've indicated the bear's age several times, you don't really gain anything by repeating it here. It should be "sank" instead of "sunk," and the repetition of "down, down, down" seems a little too forcibly poetic. Consider something like:
The slab had been diminishing since breaking loose from the glacier not long ago. Now it split in two, tipping the exhausted bear into the water, where his lungs filled as he sank beneath the surface.
continuing...
A few hours later, the two halves of his ice had lost half their mass. Half a day later, they had melted completely, leaving a bleak, cold expanse of water stretching across the horizon.
The timetable here seems a little too quick--would ice melt so quickly in the arctic? I'm asking honestly, because I just don't know. But it seems conspicuous to me, even if true. In any case, what's the rush? Change "hours" to days, and "half a day" to a "week," and the effect is the same. "Vanished completely" is more or less redundant--most things don't "vanish partially" or "vanish a little bit."
More basically, I wouldn't refer to it as "his ice," because that implies ownership that doesn't really exist. In fact, it seems stronger to me if the ice is an impersonal, independent object. Consider:
In days half of the ice was gone, and in a week it had vanished. A bleak expanse of water stretched to the horizon.
======================================================
Don't take my comments too hard--this is a nice piece with a lot of potential, though I think that you're currently in danger of overplaying your hand. Avoid the traps of anthropomorphizing, being careful not to over-write your imagery, and I think that you'll come up with a nice completed work. There's a nice resonance between the vanished ice and the vanished bear--that's your strongest point. If you can keep the reader's focus on the event without making it maudlin, you'll have a much stronger poster-bear for global warming than you'll have if you try to get into the animal's thoughts.
And, of course, you are free to use or reject any and all of my comments as you see fit. My text suggestions are rough offerings that you may likewise embrace or discard.
Thanks for sharing your work, and keep us informed of your revisions!