The style of "To Build a Fire" is typical of Naturalist literature, which tends to be highly objective and observational. London's diction is direct and straightforward throughout—he usually "tells" rather than "shows," making his rare usage of descriptive or figurative language more impactful.
The language of the story is also repetitive. London frequently references the coldness of the climate and the advice of the old man at Sulphur Creek, and his descriptions of the actions the man takes to warm himself verge on redundant:
He pulled on his mittens with his teeth, and threshed his arms back and forth, beating his hands with all his might against his sides... After a time he was aware of the first faraway signals of sensation in his beaten fingers. The faint tingling grew stronger till it evolved into a stinging ache that was excruciating, but which the man hailed with satisfaction. He stripped the mitten from his right hand and fetched forth the birch-bark. The exposed fingers were quickly going numb again.
London's repetitive style reflects another key aspect of Naturalist literature: determinism. By continuously describing how the man tries and fails to warm himself, London showcases the uselessness of the man's efforts and suggests that his fate by freezing to death is inevitable.