We can only train horses to do things they have the ability to. Yes, we can train them and make them stronger, more supple, more eager to work. But we cannot train a horse to do a back flip.
Every time we sit on a horse, we upset his balance. This doesn’t mean that the horse cannot, after training, do almost as well with a rider than without. What it means is that we should train the horse in hand first, so he has the opportunity to find his balance without a rider. This gives him the opportunity to start building the right kind of strength and flexibility for whatever it is he will do later under a rider.
Let’s train our horses so that they have the best chance to succeed! When the horse learns that people never ask him to do impossible things, his trust in both people and cooperating with people will grow.
Yes, you can train a horse to piaffe in a forward-down-out stretch. Even a fat little pony, provided his conformation makes it possible.