From the second half of the novel.
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The man from the very beginning does not listen to the oldtimers; he acts as if he knows much more than these more experienced wildnerness men. He should have been more careful on the frozen water; he needed to be certain that the traveling conditions were safe. Since he does not use appropriate precautions, his stupidity foreshadows that he cannot survive in this environment.
I think the fact that once a body part gets wet in the snow, the extreme temperature would cause frost-bite in a matter of minutes. I like the following quote in the beginning of the story. It describes his spit turning to ice before it hits the ground,
"As he turned to go on, he spat speculatively. There was a sharp, explosive crackle that startled him. He spat again. And again, in the air, before it could fall to the snow, the spittle crackled. He knew that at fifty below spittle crackled on the snow, but this spittle had crackled in the air. Undoubtedly it was colder than fifty below—how much colder he did not know."
This prepares us for the severity of the situation when the man gets his foot wet.