I have a harrris, a red-tail and 3 horses and haven’t used them together. I have worked them together and can now call my birds to the fist while on the horse without either the bird or horse freaking out. The problem is my birds are rabbit hunters and the rabbit fields don’t make for good horse fields. I guess squirrel hawking would work out better since the woods are a little more open.
My property backs up to a few hundred acres of farm land that has a pretty good population of quail. If I had a coops and a good dog I would probably saddle the horses up and use them locally. I doubt I would trailer them off my property to hunt. It is just too much of a hassle to do that.
You also better have a dead broke horse to make it all work out. You better not have a horse that will walk/run off when you get off and drop the reins. Remember you could have a bad hawk day, a bad horse day or a bad dog day. And heaven forbid they happen all on the same day.