In Jack London's "To Build a Fire," the speaker uses exposition to describe the setting and prepare the reader for what's to come.
The first three paragraphs of the story certainly serve as exposition. The reader learns where the character is (the Yukon, on the Yukon trail); the weather (clear day without any sun and bitter cold); what the man is doing (traveling on foot), etc.
Setting also includes what characters know in a story, and we get an important bit of exposition about what this character knows or doesn't know. I quote from paragraph three:
But...the tremendous cold...made no impression on the man. It was not because he was long used to it. He was a newcomer....The trouble with him was that he was without imagination. He was quick and alert in the things of life, but only in the things, and not in the significances. Fifty degrees below zero meant eighty-odd degrees of frost. Such fact impressed him as being cold and uncomfortable, and that was all. It did not lead him to meditate upon his frailty as a creature of temperature, and upon man's frailty in general,...
This exposition prepares the reader for the character's eventual trouble.
The falling action of the story occurs in the last two or three paragraphs of the story, once the man has surrendered. By then, he knows he's going to freeze one way or another, so he might as well behave with dignity. He thinks of the old-timer who had warned him, and soon freezes to death. The dog waits as long as he can, then trots off toward the next camp.