Physically, the dog and the man are both dying from the cold. It is so cold that they are caked with ice.
The frozen moisture of its breathing had settled on its fur in a fine powder of frost, and especially were its jowls, muzzle, and eyelashes whitened by its crystalled breath. The man's red beard and mustache were likewise frosted, but more solidly, the deposit taking the form of ice and increasing with every warm, moist breath he exhaled.
Mentally, both the man and the dog are aware that it is too cold. They know that they are going to die soon because the temperature is too cold for their bodies to sustain. The man has “sharp consciousness of a condition of very cold” and the dog has “brute instinct” only, but they both know that it is too cold for them to survive.
The cold and the emptiness of his surroundings has reduced the man to an animal-like condition, making him survive on instinct like the dog. Yet he does not have the instincts of ancestry the dog seems to possess.
The dog was disappointed and yearned back toward the fire. This man did not know cold. Possibly all the generations of his ancestry had been ignorant of cold, of real cold …. But the dog knew; all its ancestry knew, and it had inherited the knowledge.
Both the dog and the man know that warmth is their only hope and their only protection. They know that the man needs to provide it. The dog relies on the man to have it. The man envies the dog his coat, but the man has to build the fire. Unfortunately, he fails in his task. He gives up, and the result is his death. The dog does not understand this, because he is failing his contract with the dog. The dog cannot start a fire. It does have survival instincts of its own though.