Concerning the dog's point of view in London's "To Build a Fire," the question isn't as unusual as it may seem, since London was quite fond of writing stories from a dog's point of view. Also, this is the kind of question that gets you to think about the story and what the dog sees, but there really isn't a correct or incorrect answer. You can probably write anything that is serious and thoughtful and do just fine.
With that in mind, I'll suggest some ideas and ask some questions that you can keep in mind if you like:
- As London would write the story, the dog would probably make value judgments about the kind of master the man in the story is. Is the man gentle and kind, or does he beat the dog any chance he gets?
- Does the dog see the man as knowing what he is up against? Does the man respect nature and its power? The dog is a part of nature, in a sense, in that he is more fit to survive in the cold conditions than the man is. What does the dog think about the man's feeble attempts to survive?
- Why won't the dog go to the man when the man calls him near the end of the story? What does the dog sense? How does he know not to trust the man at that point?
- How does the dog feel when he takes off to head to the next place of warmth?
The thoughts and questions above should help you write a thoughtful piece.
By the way, just in case you mean something a little different in your question than what I've interpreted, technically, telling the story from the dog's point of view would be using first-person narration if you have the dog actually doing the talking or writing, or third-person limited omniscient, if you have a speaker telling the story from the dog's point of view and reading the dog's thoughts.