My horse background is primarily ranching, racing, and polo, but I did get the opportunity of riding 3- and 5-gaited horses while working a contract in So. Carolina. What a treat!
The training encourages specific muscling that results in their desired gaits. The same as a TBs training (hopefully) results in speed, and a cutting horse's training results in their moves.
In addition to lessons (and my daughter showed) we got to take some of the horses at the barn in So. Carolina out on little trail rides just to give them a change of pace (although the horses got paddock time daily). Delightful horses. Great manners. Very easy to work with.
I'll admit, I used to think the smiles on the faces of show competitors had to be phoney. But, after riding Saddlebreds I found it was almost impossible NOT to smile. Very fun to ride.
As a therapist I can see that when I prescribe specific exercises, with weights and bands, I'm doing the same thing as horse trainers. Targeting specific muscles to get a desired movement.