Some take to it better than others, but most can be broke. When a kid I used to find a fresh plowed field with nothing yet planted in it. That way, if I actually got thrown, it didn't hurt much. After not too many rounds the horse usually accepted the new addition to the routine and all was well.
My friends and I found that we could bend a little over the saddle, and ride right up on a pond of geese and or ducks. And we started killing a lot more geese and ducks with that tactic. I not sure what the game warden would have thought about it though. This was back in the 60s and early seventies, long before action shooting, but I doubt horses are any different now.