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One of those cases where i can recall nearly the entire story, but not the Author or the title.

• Two Pilots land on a frozen planet (Pluto i think?)


• The landing thaws the ice, and it subsequently freezes trapping them.


• They try to escape by brute force of the engine, but the fusion pile goes critical, and they are forced to shut it down.


• They draw straws to decide who will check out the damage beneath the engine skirt (its near certainty that if the pile has breached, they will die of lethal radiation exposure)


• the engine has in fact exploded, and the first pilot knowing he will die shortly, says his goodbyes, walks up to the top of an icy ridge, assumes a heroic pose, and takes off his helmet, freezing into a statue.


• there is a long struggle of the second pilot trying every possible scenario to rescue himself, with no success.


• eventually he decides that he too will find a tall ridge, assume a pose, and take of his helmet.


• noticing pilot one has his face and eyes frosted over from the atmosphere that froze from his helmet, he takes precautions so that his face will be clear of frost/ice when he takes off his helmet.


• in the end after becomeing a frozen statue he realizes he is not dead, and that every time the sun passes and warms him slightly he can think, albeit very slowly.


• the story ends with him regretting that he did not clear the frost from his friends eyes before he took his pose on his own ridge, and removed his helmet.

This is Wait it Out by Larry Niven. Two astronauts get stuck on the surface of Pluto.

After the fiasco with the Nerva-K, one of us had to go down and see how much damage had been done. That meant tunneling down with the flame of a jet backpack, then crawling under the landing skirt. We didn't talk about the implications. We were probably dead. The man who went down into the bubble cavity was even more probably dead; but what of it? Dead is dead.I feel no guilt. I'd have gone myself if I'd lost the toss.The Nerva-K had spewed fused bits of the fission pile all over the bubble cavity. We were trapped for good. Rather, I was trapped, and Jerome was dead. The bubble cavity was a hell of radiation.

and are finally both frozen semi-solid

Stars rolling up the sky. The same patterns, endlessly rolling up from
the same points. Does Jerome's corpse live the same half-life I
live now? He should have stripped, as I did.

My God! I wish I'd thought to wipe the ice from his eyes! I wish that
superfluid blob would come back.

Damn. It's cold.