The first name associated with a newer, gentler way of training horses that I remember was Ray Hunt. Turns out he was just the first to publicize it in the form of teaching clinics, but he learned from Tom Dorrance. Ray’s horse named Hondo made it necessary to try something new.
Here’s a great story about Ray, Hondo and Tom. I’m sorry the horse world has lost Ray, but grateful his methods live on in a few of the big name trainers whose clinics I’ve not yet attended.