A Whole Lotta Snow, and Super Chilly
You could definitely argue that along with our main man, the setting is the most important thing in this story. The story is set in the Yukon during the great Klondike Gold Rush, when over 100,000 people flocked to Canada's Yukon Territory in search of instant fortune. This mass migration brought a lot of young men into a very harsh wilderness, and a fair few of them had now idea how brutal their lives would become.
You can tell how important the setting is by how much London devotes himself to describing the cold wind and the ice crusting over the man's face: "The man's red beard and moustache were likewise frosted, but more solidly, the deposit taking the form of ice and increasing with every warm, moist breath he exhaled. Also, the man was chewing tobacco, and the muzzle of ice held his lips so rigidly that he was unable to clear his chin when he expelled the juice" (7). There's no way this story would be the classic it is if London wasn't so good at making you feel the chill of the air, and making you flex your hands to remind yourself you can still use them.
From the bubbling warm spring pools to the spruce tree that dumps snow onto the man's fire, the setting is constantly working against our man, whether it be through the "traps" of the hidden spring pools or the spruce that "capsize[s] its load of snow […] spreading out and enveloping the whole tree [until it] descend[s] without warning upon the man and the fire, and the fire [is] blotted out!" (23). The man tries his best to overcome nature, and actually does a pretty good job.
The setting is supposed to make not just a physical impression on us, but a spiritual and philosophical impression, too. It should take us out of our world of everyday comforts and remind us that somewhere out there is a harsh, unforgiving, and vast wilderness. From the very beginning, we learn that the day is not only "cold and gray," but "exceedingly cold and gray" (1), a permanent twilight with "no sun nor hint of sun, though there was not a cloud in the sky" (1). Sometimes, it can even seem like London's setting isn't even on the planet Earth, but some sort of frozen planet like Hoth in The Empire Strikes Back.
The narrator gives us a hint at how we should respond to this wilderness, suggesting that we should avoid the man's "trouble" by learning to appreciate our surroundings. Above all, we should allow ourselves to approach the Yukon setting with "imagination" (3). It should make us "meditate upon [our] frailty as a creature of temperature, and upon man's frailty in general, able only to live within certain limits of heat and cold" and eventually take us into "the conjectural field of immortality and man's place in the universe" (3). But if you're not into all that heavy philosophical thinking, feel free to plow ahead into the Yukon wilderness with our main character, thinking only of biscuits and bacon. Just be prepared not to come out the other end.