This story is designed to show the might of nature and how man is still subject to various natural forces that are beyond our control. Even though man has become the master race in so many ways, this story reminds us of how fragile we are and how nature is still stronger than we are.
Thus we can argue that the weather, and in particular the intense cold that eventually kills the man, symbolises the strength of nature. The man himself symbolises the arrogance of man in ignoring the might of nature and his own fragility. Note how the follwing quote makes reference to both the weather and the man:
Fifty degrees below zero meant eighty-odd degrees of frost. Such fact impressed him as being cold and uncomfortable, and that was all. It did not lead him to meditate upon his frailty as a creature of temperature, and upon man's frailty in general, able only to live within certain narrow limits of heat and cold, and from there on it did not lead him to the conjectural field of immortality and man's place in the universe.
Note the way that the cold is clearly linked in with the power of nature, and the man is shown to be unable to grasp his own "frailty." Interestingly, the dog, throughout the story seems to be able to do what the man cannot. He is an instinctual creature, and as such, he recognises the danger inherent in the freezing cold conditions, although the man is blind to this, having lost or distrusting his instincts. Although we are told that the dog did not know anything about "thermometers," the narrator tells us that "the brute had his instinct," which is what saves it and ensures that the man dies.