How do you describe the motion of a horse when it brakes?
I always see horses in the movies raise their front legs in the air when they are halted by the riders. How would you describe the motion when they do such thing?
What the horse is doing is rearing (up) (Wikipedia link for more than a definition). Oxford has verb (2) (of a horse or other animal) raise itself upright on its hind legs. It may be as part of a panic stop, or it might be the result of training for display as in the picture you show. In the latter case it requires skill and training from both the horse and rider; in the former it's dangerous at least for inexperienced riders, and is not normal stopping behaviour. It would be quite intimidating if you were standing near it, and would also be a way of showing off the rider's skill. It's probably just a movie stunt thing rather than historically accurate (assuming you're referring to westerns)
I don't think this is "putting the brakes on"[sic]. The riding apparel and position of the horse both suggest that this is a dressage exercise from the Spanish Riding School in Vienna.
May I refer the OP to the Google images of the Spanish riding school Vienna.
However, the chestnut horse is not that of the famous white Lipazzaner breed of horse associated with the school.
The movement that the painting depicts may well be from "classical dressage, the Levade and the Presade, in which the rider asks [sic] the horse to set [sic] well back on its hindquarters and raise its front legs off the ground to vairying [sic] degrees". (Wikipedia)