How do the man and dog approach the intense cold differently, and what point is London making with this difference?

The dog is guided by instinct, while the man must rely on human judgement, which is unreliable.

When faced with extreme cold, the dog experiences "a vague but menacing apprehension that subdue(s) it". It wants nothing more than to "burrow under the snow and cuddle its warmth away from the air". When it falls through the ice on the river trail, the dog automatically knows what it must do, and cleans the ice from his feet and legs. It is equipped by nature with a thick coat to protect it, and it can sense what it must do to survive.

The man, on the other hand, must struggle against nature in order to make it. He has to make choices, the most critical of which is his decision to set out into the Klondike despite warnings of danger. The man must rely on his own initiative and employ the trappings of civilization, and he is hindered both by his failure to prepare properly for his journey and his proud refusal to listen to the Old-Timer, the voice of experience. His misjudgements are costly, and the man does not make it out of the wilderness alive.

The point London appears to be making is that man is insignificant in the face of nature, his environment. Man approaches nature as an adversary, and his chances of coming out ahead are questionable. In contrast, the dog is one with nature, and nature takes care of its own.