A suicide, Clinton style?
I wonder why the killer(s) didn't steal his stuff. Resources in the 10,000 foot high mountain pass would be a bit sparse. I would think they would take anything useful they could find.
If the arrow was not immediately fatal, he may have hidden and died later.
Even today with modern rifles hunters lose game animals that are only wounded, run off and die in hiding.
An adversary capable of mounting an ambush and fighting back would certainly slow the search.
Hit him with an arrow in the evening, he hides and dies, which his pursuers don't know, a little snow overnight, and looking for game at lower elevations starts to look better and better in the morning.