How does the man's struggle with the dog illustrate both Man vs. Nature and a Man vs. Self conflict?

Man vs Nature has little to do with the dog. The dog is an example of Nature and he can last more easily in the cold than can the man. The man vs Self conflict is not as big as Man vs Nature and Man vs others. The man does not listen to the experienced people who know just how cold it is; the man goes out in the 70 below temperatures when he has been warned.