Horse riding was updated since the release version to be better, so there's a difference in riding (and it may contain the speed of horses as well; as I played the release version for some time and I felt the horses are bit slower there).
And to horse bravery stat, IDK. I think it exists and even if you have a same two horses (like two silver mustangs, even the same gender); one can be the bravest horse you had and one can be scared even of squirrels and dogs.
I had that experience with one mustang and I explained it in this post (if you're interested).