It is of course the unfortunate unfailure of the anonymous protagonist in this excellent story to pay attention to the advice that the old man from Sulphur creek gave him before he embarked on his journey that results in his death. The first mention we have of the old man is when the protagonist remembers the old man telling him precisely how cold it got in the country, and then how he had actually laughed at the old man. Listening to this advice would have probably causes the protagonist not to venture out in the first place, as he would have had a healthy respect for the cold and how dangerous it could be.
Secondly, the old man told him that "a man must not fail in his first attempt to build a fire--that is, if his feet are wet." This is one piece of advice that the protagonist does listen to and act upon when he does get his feet wet after he falls through the ice into water.
Thirdly, the protagonist remembers another injunction that is given to him by the old man:
He remembered the advice of the old-timer on Sulphur Creek, and smiled. The old-timer had been very serious in laying down the law that no man must travel alone in the Klondike after fifty below. Well, here he was; he had had the accident; he was alone; and he had saved himself. Those old-timers were rather womanish, some of them, he thought.
Note the arrogance of the protagonist in the way that he rejects this bit of advice, and rather insultingly considers the old-timer to be "womanish." This is another crucial bit of advice that could have potentially saved the protagonist, for travelling with a companion would have meant there would have been somebody else to help make a fire or fetch help. The protagonist's arrogance is yet again shown to have led to his death.