The crux of the story deals with the harsh and merciless side of nature where "only the strong survive." The man in the story is obviously a newcomer: he 1)travels alone (only in the company of his dog), 2)is underequipped ('travelling light') and 3)lacks foresight. Besides all that, he 4)is physically inept, as portrayed when he stumbles and falls into the river.
Drenched to the bone, he makes his final mistake of building a fire under a cedar laden with snow, which when heated, slushes off, thus putting out the fire underneath. As he had used his very last match, the man freezes to death.
Although Jack London was Canadian (and not USA 'American'), this short story is an example of the naturalist tendency in American literature at the time. In naturalism as a literary genre, nature is depicted as a hostile force which pits itself against the intelligence and instinctive wisdom of man. The protagonist in "To Build a Fire" falls very short in both of these categories and pays with his life.