When I looked at the video, the very first thing that popped in my head is why is he moving like that. The video is n't great with him being ridden in the snow. I didn't notice the reins being held that tightly, but I though the head being pulled in that harsh was odd. Also, he's not under tack, I'd echo the sentiment that he should be tacked up and ridden with a saddle. Some horses are great bareback, but put a saddle on them and they act stupid.
Secondly, the wraps are horribly done. I would also be concerned that they are covering up a flaw. Folks who use wraps regularly, don't do it like that! Also I don' like the way he moves out when they jog him. It really concerns me that he may have a back issue. he just seems uncomfortable.
He may be a sweet horse, but all I can think is - medical issues. I may be wrong. It may be a really bad video with really inexperienced people, but It's itching the back of my brain that something in underlying here.