I carry my Glock 29 whenever I'm out there. Also have my GSD for company.
We hike the less used trails and drive the old logging roads. In the past 15 years, I've never seen anything that made me concerned, but I'm always glad to have Mr. Glock with me. I usually carry open in the summer and concealed in the winter simply due to the type of clothing I'm wearing. I'm aware that open carry isn't really "permitted" but it's so seldom that I see anyone on the trails that I don't worry about it. On the roads, I think I once saw a sheriff's deputy and two or three times, a FS LEO who patrols a huge area. Unless you visit established campsites, recreation areas, or the most popular trails, it's very unlikely you will see many people or LEOs. (Deer season is the exception.)

Last year, we were lucky enough to see three black bears. Two ran from us and one, a mother with two cubs, never saw us. Was a real treat to watch them for a few minutes as they crossed the trail, about 40 yards ahead of us. (The wind was blowing toward us. Otherwise, we would have never seen them.) Also lucky that my GSD doesn't bark much in the woods. He sat quiety, watching them intently.
I did keep my hand on my Glock the entire time, just for safety sake.

It's a beautiful area and great for recreation. But, the unexpected can always happen so we should be prepared.