I live in cougar country and have never even SEEN a cougar. I would love to see one (everyone looks at me crazy when I say that) but honestly, I would love to see one.
I never even think about cougars when I ride (other than hoping maybe one day to see one).
In the summer I usually have a friend or two to ride with, but in the winter I almost always ride alone.
We see lots of elk, turkey, deer and javalina. I recently saw my first black bear (when we were driving a dirt road on the way to find a place to park and ride).
My main concerns when out riding on the national forest are not getting lost and not getting shot during hunting season.
Wildlife is a joy, not something I worry about. (I always carry at least one elk call so I can talk to the elk if I see them.) I feel safer on a horse than on foot, because while I feel I might not notice something on foot, I feel pretty confident that on horseback between me and my horse, we see and smell most everything.