Not being particular familiar with horses, other than a few trail rides in the distant past.. I have a question.. HOW do they get the horses to prance like that? And lift their legs so high.. It does not appear to be their natural gait.. Just curious.. They are so beautiful though.
I'm no expert on the training procedure of course, but it's probably something like this (and if anyone has a clearer understanding, I'd appreciate learning from them too.
First of all the trainer would look for a horse that already had a naturally higher step at a trot, then from the ground, as the horse stepped forward, he'd give it a very light tap just behind the forelegs and would use a specific cue word for each leg. The horse learns the cue word as time goes by and then with a rider on, using the words to signal, would move the horse out at a walk and begin including little seat and toe signals. Also it's important to teach the horse to keep his head high which makes him round his back, which causes him to move with his butt more under him. This lightens and centres his balance so that his front end and back end are freer to move those legs easily.
I would guess to that in teaching them to lift a little higher than is the norm, you might proceed with a light tap-tap-tap to keep moving that leg up just a bit more each time and then when you stop tapping, they could put the leg down.
Then as the rider is on board, he'd also be using his seat (shifting ever so slightly from side to side, back or forwards) and would use toe or heel pressure or just the slightest touch to signal the horse. It's absolutely amazing how you can direct all four quarters of a horse, plus their balance with movements so subtle that the average watcher sees very little movement from the rider. Even a twitch of the reins can send a signal so the riders hands should be still and quiet.
Some horses are naturally willing and interested in the learning and others resist because they're just obstinate. My one mare was very willing, but easily upset, so working with her was easy as long as I was patient and gave her time to understand. The other was, well let me put it this way, her nickname waffled between 'our magic pony' and 'the old grey hag'. It took about five minutes to train the first one to step over sideways at a gentle touch of my fingertips (just brush against her sides) whereas the other (our sweet 'hag') I finally had to resort to using a rounded spur to put pressure on her rib cage because she ignored my aching finger tips entirely. Her attitude was, 'I can outlast any pressure you can lay on me'. Keep in mind that you start with the lightest pressure, then if they don't respond appropriately, you push a bit harder and hopefully they move away at that point. But through it all, they are the one who decides how much they will resist, they make the choice. The point of this kind of little exercise is to get them to move over or away from pressure (so I didn't get squashed against a wall or to get a foot off my toes)....so the minute they step over, you take the pressure away and that's the reward to them. Do this a few times and they get so that they learn to respond to that first light touch. Unless they are the sort who challenge you on everything which Ambra was.
And I'm glad you enjoyed watching Blue Hors Matine. Unfortunately about five years ago she broke her leg in the field and had to be euthanized. But you got to see her at her finest!