Also, just throwing this out there to make people sad, but…
When he’s thawed out he’s laying down. He was frozen laying down. And the plane hit the water when he was in the pilot seat- we saw that.
Which means he wasn’t knocked out by the initial impact. And it doesn’t look like he drowned, either. He had time to see his expected death coming, after the impact, and lay himself down. My guess is some internal injuries from the crash, followed by freezing to death inside the plane.
So just go ahead an add a little scene in your head of Steve surviving the crash, but knowing that wet and isolated on a field of ice, in a plane that’s still sinking, nobody would get to him in time. But he knows he’s done his job. So he lays down, and closes his eyes, and maybe wonders if anyone will ever find his body, and bring it back to be buried by his mom and dad, since Bucky never was buried. But either way they’ll have a service for him, and that will be nice, and the priest will say the words and he’ll be at rest. And he feels bad, leaving his men, and he regrets everything he never told Peggy, and that he won’t be there for her now, but at least he did his part, right? He got the job done, and that’s what counts. If he dies alone, bleeding out and freezing, that’s all that Bucky got, to. So that’s all right.