I would argue that "To Build a Fire" suggests that death is inevitable in certain circumstances, despite one's best efforts to stay alive. It also reminds us of the importance of heeding warnings that could potentially save one's life.
The unnamed narrator in this story was warned about the danger of travelling through the extremely cold area, so it cannot be argued that he was unaware of what he was getting himself into. The story therefore suggests that in order to conquer death, or at least to live a little longer, we should heed the advice we are given.
Once the man gets into trouble, falling through a thin patch of ice, he takes proactive action to prevent death. He is well aware that he will freeze to death if his feet don't dry, so he builds a fire in an attempt to stay alive. His efforts are thwarted, however, when a pile of snow falls from the boughs of a tree, smothering his fire. Frostbite has, by now, set in to the man's fingers, rendering him unable to light another fire. He is powerless, by this stage, to do anything to save himself and is struck by the inevitability of death.