You have hit the nail on the head when you say that it is the "old-timer from Sulphur Creek" who gave the man "key advice." It is so very "key" that, if the man would have listened, he would have still had his life at the end of the story instead of freezing in the frigid temperatures.
It is simply luck that the man meets the old-timer before his adventure in the Yukon. In the back of his mind, the man knew the Yukon in the winter was dangerous. The old-timer continually emphasized the cold, especially in "the country." The man is already in trouble in that he "laughed at him at the time." Still, the old-timer goes on with the most important part of his "key advice" you speak of in your question. He mentions the importance of taking someone else along (so that the man isn't in the wilderness alone). He mentions the importance of keeping one's feet dry. Then he says this about the cold:
There must be no failure. When it is seventy-five below zero, a man must not fail in his first attempt to build a fire - that is, if his feet are wet...the circulation of wet and freezing feet cannot be restored by running when it is seventy-five below.
We should get from this how absolutely imperative it is to build a fire right away in case one's feet get wet. Again, the man laughs. Full of pride in his own abilities, and unwilling to listen to the wisdom of the elderly, the man sets off.
Unfortunately for the man, he only takes into account the wisdom of the old-timer when he is approaching death, freezing in the extreme cold of the Alaskan wilderness. How do we know, as readers, that the man finally realizes the wisdom of the old timer? Because the man, dying, says this:
If he had only had a trail-mate he would have been in no danger. The trail-mate could have build the fire.
Thus, the man dies alone in the wilderness due to his own negligence.