He is a very nice looking horse! Hard to tell on such short clips - but I got the impression that he was a bit tight and bundled up - was there some tension and anticipating the canter/walk?
I would play around at home with canter to a shoulder fore, keeping the canter a bit more active (as paula says, he needs to learn to be collected) and then transition to walk from the shoulder fore - it will help you balance him in those down transitions. Then, while schooling, let him take several active walk steps - I’m not seeing 3 pure, well-defined walk steps in any of those examples - so while schooling, give him more time to walk so he’s comfortable with that concept. My boy use to get really tense in these transitions, so we do the canter to walk, then I’d give him a few steps of free walk, before back to contact, and then canter - ultimately, his walk became MUCH better in between.
