Fred Bear was probably just imitating his mentors when he started wearing one. You can find old pics of Saxton Pope, Art Young, Chief Will Compton, and all those old guys wearing fedoras, because it was the general fashion then. I can remember even when I was a kid, almost every older man wore a fedora hat. I've been known to wear one, too. I guess it's just another outmoded traditional behavior that has been retained as part of the culture by trad archers. Plus, they are quite functional, good hats.