The "old-timer" in the story gives the man a very important piece of advice that he chooses to ignore. According to the old-timer on Sulphur creek, "No man must travel alone in the Klondike after fifty below." This was for safety's sake. When conditions are that cold a man can die very quickly should anything happen. Traveling with a partner can save your life.
At first the man actually scoffs at the advice "Those old-timers were rather womanish, some of them, he thought. All a man had to do was to keep his head, and he was all right. Any man who was a man could travel alone." But after the snow falls on his fire and puts it out he realizes the geezer was right: "Perhaps the old-timer on Sulphur Creek was right. If he had only had a trail-mate he would have been in no danger now."
So there's your answer. The man ignores the old-dude's advice to never travel alone when it was so cold out.