Why is he traveling light without many supplies?

To some extent, this is an opinion-based question because the story does not expressly say why the man was travels light. It is up to readers to determine why he is traveling that way based on the details given. I have some possible reasons that I think are all responsible for why the man was traveling light.  
1. He is ignorant of what he might need in the frigid Yukon. Readers are told that he is new to the area, and this is his first winter. The man simply doesn't know that he should be better prepared.  

But all this—the distant trail, no sun in the sky, the great cold, and the strangeness of it all—had no effect on the man. It was not because he was long familiar with it. He was a newcomer in the land, and this was his first winter.

2.  He only plans for what is right now. He does not know how to plan for what might happen. The story tells readers that he doesn't have the ability to imagine. He knows it's cold, but he can't imagine exactly how the cold might cause him problems.

The trouble with him was that he was not able to imagine. He was quick and ready in the things of life, but only in the things, and not in their meanings.

3. His companions already made the trip, and the man is counting on an equally uneventful trip. He is counting on having no problems, and he is expecting to arrive at a camp that already has supplies and food. He sees no reason to bring extra.

He would be in camp by six o’clock that evening. It would be a little after dark, but the boys would be there, a fire would be burning, and a hot supper would be ready.