The most trainable horse I have yet ridden is a National Show Horse-- half-Arab, half-Saddlebred.
He’s not built to do dressage and had a history of bad training plus a wreck that makes this kind of work hard for him. But, man, he’s Got It Going On between the ears. This horse likes people (even though they have mistreated him), wants to please, will try hard and is smart, smart, smart.
You say “Not that… not that… not that… yes THIS— this is what I wanted” and he latches on, offering you that “Right answer” again. And he’ll do that from one ride to the next, no matter how far apart. If you can show him what you want, point that out to him and get off, he’ll start there the next time you get on him… 5 days later. Remarkable.
For your purposes, OP, if this horse’s breathing and physical soundness check out (and my old, broken NSH is way sounder than he should be), check out his brain. If you like the brain and the personability he offers you, take him on.
I think this horse can do lower-level dressage OK. And he’ll be a project, but I find this Smart, Friendly, Wants To Please NSH mind is a great one of have on your team if you have a long-term training project. I’d sign up for a remedial NSH as opposed to a remedial cold-blooded WB or stock horse breed any day. The remedial, not-built-well horse needs a whole bunch of “want to” in order to overcome his body’s limitations.
ETA: This horse also is forward-thinking, a crucial characteristic for the dressage horse. These “toward saddle seat”-bred horses have that. And they appear to be hot or reactive. Actually, they are not. They will give you the impression of being ready to explode and actually have a lid on it, mentally speaking. Those of us who grew up with the Thoroughbred mind think that saddle-bred types are always about to lose it… when they are not because they have been bred for a mind that is spicy but smart.
So if you want a horse who is a push ride, the NSH or this one isn’t it. He’ll scare you as you work with him. That’s because in order to get him to use his hind end and back, you’ll have to Go Forward. And that will seem physically- as well as mentally fast to you on this kind of horse. But if you put this kind of horse in, say, a big, forward, pushing into the contact trot, he’ll most likely stay there and not leap around. In other words, he’ll be rideable, even at speed and with impulsion.
The people who get into trouble with a “saddle-seat-bred” forward-thinking horse are the people who want to choke them down. So, IMO, people trying to rush to collection and make Arabians (or show-bred Morgans for that matter) into Western Pleasure horses are the folks who screw these horses up mentally and physically.
And that’s the kind of the ride you see in that first video. Except, I the rider’s seat suggests that he rides saddle seat but happens to be sitting in a western saddle. These horses can’t do that in the mind (without the very focused training that dressage offers; they have to be taught to ask for direction every stride… it doesn’t come naturally to the forward-thinking horse, even if he’s smart.)
And the big issue is that collection takes hind-end strength and core strength that these horses were not bred to have in their conformation. So it’s physically harder for the horse who has a high head, low sternum (his carcass is downhill between his shoulder blades, regardless of how vertical his neck is), and trailing hocks. That conformation is selected for trotting in harness. It’s not good for much else, IMO. It makes the walk and the canter hard. It makes using the hind end for collection or jumping hard.
So you CAN create a saddlebred-built horse who can do legitimate collection and who can tuck that straight pelvis and trailing hocks underneath him. But you must do that via correct dressage training, with No Short Cuts. You must ask for forward-- using the hind end and the lower back first. You must teach this horse to seek the bit, wherever it is-- high or low, reins long or short-- and to push into it… so that you have a way to get him to lengthen and use is back when he’s going forward. You must get that power to come from the back feet pushing all the way through up to the bit.
You have to do this on horses with this conformation because it takes more “going to the gym,” plain, old strength building for them to do collection than does a horse with a skeleton equipped with the angles that make collection easier. They’ll need to be comparatively stronger than the better-built horse in order to deliver, say, the same slow canter or the same decent downward transition.
And when these horses worry, it’s often because it scares them to be asked to do something they feel they can’t sustain because they just aren’t strong enough. IMO, that’s how you get to fake, worried collection in this kind of horse who is trained to look like the very different AQHA WP horse.
Hope this gives you a better sense of what this horse might require so that you can decide if he’s a project you want/can ride with safety and pleasure.