I see a few moments of the head bobbing up and down, not side-to-side.
Up and down indicates a running walk.
It's hard to tell from such a short blurp, but the horse almost looked like it wasn't sure what to do. OP please don't take offense and I could have been seeing things totally wrong, but it looked like the horse KNEW what to do, just couldn't because it was getting mixed signals.
That might account for folks thinking it was performing the Step Pace; I do have one horse that does the Step Pace and there is no question that his head moves side-to-side. The head in the video appeared to be going up and down - at least from the angle of the camera
Stepping Pace, rack, hard lateral pace, the head always moves side-to-side.
In either case, the degree of head movement varies with the horse.
Did the OP have to set the camera on a stand and take this video herself? That would explain why there was so much "empty space" in the video.
It would be great if someone else could do the video so the horse could be filmed in for a decent period of time
And no, he doesn't need shoes. If you have a good trimmer and he's only going to be ridden on the farm - what's the point
I have one TWH that has only worn shoes once or twice in his life, when I knew he was going to be ridden in extreme rock and shale conditions.
He has that champagne-smooth running walk that people lust after --- and a barely grade one club hoof. He's now 16 and has been with me since he was 2-1/2. He has never come up sore from being ridden barefoot
Can you drag someone in off the street to help you get a longer running video of him?