As far as stabilization goes, there are breeds of horses which are almost completely bounce-less. There is no jarring action that a quarter horse has at a trot with say a Tennessee Walker or a Racking Horse. It's more of a side to side "sashay". If you were going to attempt to film from the back of a horse, I'd explore the idea of getting a gaited one.
The only problem is that we don't have gaited horses for you to try out. As far as hunting horses go, we have quarter horses - not the smoothest rides. I seriously doubt you'd want to try to film from the back of my high energy show mare (pictured). I would think that if you tried hunting horseback with us or someone else and liked it enough to get a horse, we should locate you a gaited one.
M
