In general, each time the man remembers the old man's advice, it's either to acknowledge the old man was right, or to consider the old man "womanish". As you can see in the quotes below, he had to admit the old man was right more than he could say he was wrong.
All this the man knew. The old man on Sulphur Creek had told him about it, and now he was grateful for the advice.
He remembered the advice of the old man on Sulphur Creek, and smiled. The man had been very serious when he said that no man should travel alone in that country after 50 below zero. Well, here he was; he had had the accident; he was alone; and he had saved himself. Those old men were rather womanish, he thought.
London is trying to convey the idea that the Old Man had respect for nature: he had the imagination to know what nature can do if not respected. The man lacked this awareness.