The man
The man in "To Build a Fire" is purposely not given a name, as the deterministic environment is more important than his free will and individuality. His goal at the start of the story is to reach the camp to meet "the boys," presumably to prospect for gold. The man's greatest deficiency, leading to his death, is his inability to think about the future consequences of present actions or facts; at the beginning of the story, London describes how the extreme cold does not make the man meditate upon mortality. More pertinently, the man does not realize that building a fire under a spruce tree may be dangerous. In all his actions, the man exercises only intellectuality--he thinks about the temperature in terms of degrees Fahrenheit, for instance, a scientific indicator. He never uses instinct, which would inform him without thinking that certain actions are dangerous. The dog, conversely, instinctively understands the danger of the cold without knowing what a thermometer is. Ultimately, the man's lack of free will exonerates him from any deep responsibility for the accidents he has, which is why London writes that the second accident was his "own fault or, rather, his mistake." A "fault" implies full responsibility, whereas a "mistake" suggests an isolated incident out of one's control.
The dog
The dog represents pure instinct, a trait necessary for survival in the harsh Yukon. Unlike the man, who requires the products of intellectual civilization--warm clothing, matches, maps, thermometers--the dog simply uses its own natural advantages--fur, a keen sense of smell. Perhaps more importantly, the dog has an instinctive understanding of the cold. It knows that such conditions are dangerous and unsuitable for traveling; when its feet get wet, it instinctively bites at the ice that forms between its toes. This sense of instinct preserves the dog as opposed to the man--it even knows instinctively when the man is attempting to kill it (to warm his hands in its carcass). Although the dog cannot create a fire for itself, or even hunt down food in the wild so well, its instinct keeps it alive and allows it to find the nearby camp of men--"the other food-providers and fire-providers."
The old-timer
The man remembers the advice of an old-timer from Sulphur Creek who warned him against traveling alone in the Yukon when the temperature is lower than fifty degrees below. The man first scoffs at this advice when he adeptly handles his first accident, but later understands the wisdom in the old-timer's caution: man is not instinctively fit for the harsh, indifferent environment of the Yukon.
The boys
The man is trying to meet "the boys" by six o'clock at night. Presumably, they are prospecting for gold. Though they never appear in the story, the boys (and the man) are examples of the lower-class characters naturalism turned its attention to; only men without much to lose would risk their lives in the harsh Yukon.
