I agree with the first post in that I do not think this story is really about communism. However, if you really have to find communism in this story, here are two possibilites (though I really think both of these are reaching a bit...)
- The story is a criticism of the capitalist idea of rugged individualism. The man thinks he can go it alone, just as people in capitalism think that they can simply compete alone against everyone else. This individualism ends up getting him killed.
- When he tries to build the fire under the tree, he disturbs the tree by pulling twigs and such off it. The tree then dumps snow down and puts out the fire. You can take this for a metaphor for capitalism destroying itself. Capitalists pull at the tree of society (the workers) and ignore the fact that this can upset society and cause the destruction of the capitalist system (or at least this is what Marxists say will happen).
Again, I think these are a bit of a reach, but it's the best I can do for communism in this story.
Unfortunately I don't really think this excellent short story has much to do with communism. I wonder if you are actually confusing communism for Naturalism, which is the real focus of this story. Naturalism is a philosophical movement where writers were greatly influenced by the ideas of Darwin and the surivial of the fittest. Naturalism presents human beings as subject to natural forces beyond their control, and this idea can be seen through the use of symbolism in "To Build a Fire."
One of the biggest symbols in this short story is actually the fire that the man builds, or tries to build, on three separate occasions. The fire acts as a symbol of the man's weakness and vulnerability to the cold around him, reminding him that he is subject to natural forces beyond his control. Note what the text tells us:
He knew there must be no failure. When it is seventy-five below zero, a man must not fail in his first attempt to build a fire--that is, if is feet are wet. If his feet are dry, and he fails, he can run along the trail for a half a mile and restore his circulation. But the circulation of wet and freezing feet cannot be restored by running when it is seventy-five below. No matter how fast he runs, the wet feet will freeze the harder.
Thus we can see that the unnamed protagonist's reliance on fire is actually symbolic of his--and man's--frailty when faced with the might of nature. It is the man's failure to truly realise this that leads to his death.