The mood of London's "To Build a Fire" is ominous or foreboding. Disaster is waiting to happen.
The temperature is cold, but more importantly it is colder than the traveler thought. He is warned not to travel alone, but he does it anyway. He is new to the land and inexperienced, but, again, more importantly, he has no imagination. He does not consider what could happen. He walks on the frozen water, but the covering ice is deceptive.
The traveler underestimates the natural forces he is pitted against, and he does not understand that he is at their mercy. The mood is ominous.
In many ways, the mood of the text is based on the impending disaster that is about to befall our hapless traveler. If you look at the opening of the story, much of the description of the setting actually suggests the problems that will befall him. The description of the weather, the description of the trail, and particularly the description of the dog and the way he is resisting the trip serve to highlight the coming death by cold. So I would characterize the mood as being a nervous waiting sort of mood, the calm before the storm almost.