[MRM]

That's "To Build a Fire". The protagonist was a person from the lower 48 who didn't understand the rules. He had made it through a winter or two, but he was cocky and didn't listen to the old timers. He tried to travel when it got lower than 50 below. The rule was you never traveled at 50 below; too much could happen that would kill you if you got stopped at 50 below. The guy figured cold was all the same, he could make it. Once he got going he realized it was colder than 50 below. How much colder he didn't know, he didn't have anything that could measure that far down. "He spit and it crackled frozen against the snow. Spit freezes at 50 below. It was colder than that." Or something pretty close.

He has a series of what should have been insignificant misfortunes, but because it was so cold each problem was life threatening. By the time he realized he needed to stop and light a fire to warm up and regroup, he was too cold to do it; his hands couldn't grip the matches. Eventually he got a fire started by taking a fist full of matches and lighting them all at once. That was the only way he could grip the matches. But he light the fire under a fir tree, and the warmth of the fire melted the snow in the fir bows, dropping on to the fire and putting it out.

At that point he was out of ideas. He tried to call the dog over to him with the idea of killing it and sticking his hands into the belly to warm them enough to start a fire. If he could just get his hands warm enough to get the fire started he could rest, dry off, refit and make it to the next base. But the dog sensed something strange with the man and wouldn't go near him.

The dog ran off a bit and lay down, wondering why the man didn't light a fire. He knew it was too cold to stop without building a fire, and all the other men he knew would build a fire as soon as he stopped. But this one just lay there in the snow. The man grew very cold, then felt as warm as he had ever been before he drifted of to sleep. The dog sniffed the man and smelled the smell of death and ran off to the next outpost where he knew there were men with fire and food and warmth.