What it takes to train a horse depends on the horse. Without knowing what the horse the OP posted was doing, and without seeing what happened, I don’t know if there was abuse or not. But if you have a dominant horse, then the training might not be very pretty at times.
In turn, the laws are usually written in a way that allows ranchers and those training large animals considerable freedom. As I said, in most cases, no blood, no foul in the eyes of the law.
Branding cattle (or horses) isn’t pretty, but neither is it illegal.
Gee - thanks for explaining that for me.