RD, I love that video of Merlin. I think my fave part is when they face off with the bull, it is almost like reverse cutting LOL. And talk about athlete!! How difficult does it have to be for the horse to sidepass at a gallop?!
I have had a horse get gored by a neighbor's bull while trying to get one of our cows out of the pasture. Made me sick and so mad that I could have beat the bull to death with a t-post if I'd had one. Horse survived but kept an ugly scar on his shoulder as a reminder. He would always be flighty when close to cattle after that.
I enjoyed the first video, they seem to be having fun with their horses though I didn't see anything particularly unique about it. Almost anyone with a little bit of sense and a pocket full of treats can get their horse to do that. The second vid, the one that RD posted is an example of true horsemanship. It simply illustrates how much control the rider has over the horse. Purely seat and leg cues and while there may be many people that can get their horse to do that, it is very difficult to get it that smooth. The only thing that I don't particularly care for is the frame that they keep, similar to a dressage horse. I like horses that work long and low but that is simply a personal preferance.