What is the conflict in "To Build a Fire"?
There are several conflicts in the story. One is man vs. nature, the main character's struggle to survive in the wilderness. He isn't experienced traveling in the Klondike and doesn't take the necessary food and supplies he needs to survive. He also ignores the advice of veteran travelers who tell him never to travel alone when the temperature gets below minus fifty degrees. Our traveler doesn't respect the forces of nature and how cruel it can be.
Another conflict is man vs. death, coming to terms with one's own death. The main character must accept his death and goes through different stages before he can come to terms with it. He berates himself for not listening to the old-timer's advice, then becomes depressed, goes into a panic, and then makes one last attempt to survive. His last act is to "try meeting [it] with dignity", accepting that his death is certain.
I agree that Man v. Nature is a central conflict to this story. However, the most crucial conflict is Man v. Self. This man's overblown sense of capacity is what leads to his death. London is investigating what happens inside every tragic mistake in a classic tragedy. A quest is pursued, however, despite warnings the "hero" misinterprets signs and symbols and finds himself reaching beyond his grasp. This costs all tragic heroes their lives.
He is "quick and alert to the things in life, but not their significances"... the traveller cannot mesh his sense of self with the cruel universe in which he lives. Even in imagining his own death he still thinks it will make quite a story when he gets back to friends. It is a perfectly illogical mindset. London is saying we all have it and it is our greatest flaw.
Another conflict is man vs. animal. This is because the man did not trust or let the dog find their way to the camp, when it is clear the dog could have led the man. The man insisted on control and was domineering with the dog. Instincts in the dog were much more valuable than the man realized! If he had survived, the man might have realized that he should have "listened" to the dog in the first place.