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There is actually only one character in the story, unless you count the dog. The dog acts instinctively, the man doesn't have the same instincts and places too much emphasis on what he thinks he knows. The dog is cautious.... the man is foolhardy.
For example, the man decides to kill the dog, so he can warm himself within its body. The dog senses his intent and is frightened by his voice.
Another example would be the dog's ability to warm himself and clean the ice off of his paws and legs when he breaks through into the creek. The man needs to dry everything off and doesn't pay attention to where he's building his fire. Thus, building the fire is impossible.
To Build a Fire