When the man builds his fire under the tree, snow falls on it from the boughs.

The man is really struggling because he does not seem to have outdoorsman skills.  He stumbles his way into the limited shelter of the tree, and that is where he chooses to build his fire.  After it begins to crackle, he looks up and realizes his mistake.

Now the tree under which he had done this carried a weight of snow on its boughs. ... Each time he had pulled a twig he had communicated a slight agitation to the tree—… an agitation sufficient to bring about the disaster. 

The snow falls, inevitably, and lands on the man and the fire.  Of course, that’s the end of the fire.  The man is “shocked” and feels like this is his death sentence.  He can’t survive out here in the wilderness without a fire.

London depicts one man’s struggle for life against the perils of nature in stark detail.  One man, alone in the snow, trying to do nothing more than build a fire.  The man’s ignorance is his death sentence.  At every turn, he becomes more and more endangered by the weather and lack of protection from it.