You know, I never really had any real problems with cougars/bears while playing RDR. I never bought the game, and only played it when my brother borrowed it from a friend months after it came out, and in those months all I heard about the game, other than how great it is, is how you get blindsided every five minutes by a cougar. So naturally when I did play it, I was super paranoid about getting mauled every time I went out into the wilderness, but it never really happened.
I don't know, it could be because of how paranoid I was that I didn't get destroyed by wild animals, but with all that I heard about it, I figured it was unavoidable.