I wanted to elaborate on my last point about hind end usage by tying it into a discussion of the role of the rider in supporting their partner's correct movement.
As I mentioned last time, a horse's hind end acts as their motor, driving them forward and allowing them to extend their front legs outwards (as is the case with dressage or hunter horses) or allowing those with more forward set shoulders to roll their front legs upwards (as is the case with fine harness or saddle horses)

It is the job of the rider to facilitate their equine partner to the best of their ability. This job requires finesse and attention to detail. As a general rule I have observed that the more advanced the equine athlete, the more subtle and delicate their handlers must be. Most people seem to approach the task of riding as a separate style from that taught as "correct" equitation. Yet equitation is the art of horsemanship and is therefore designed for optimal support of the horse. This is particularly the case in regards to the animal's "motor" (their back-ends)

A rider who is facilitating their horse's anatomy allows their partner to move in the best way possible. Oftentimes we see riders with their heels forced down to the extent that their legs become shoved out in front of themselves. The rider's legs should in fact be positioned in a way that allows them to lift the horse's ribcage, especially when riding around corners where the animal's weight must naturally shift to keep it well balanced. A rider who is lifting their horse's ribcage is allowing it to raise up in it's middle back, thereby dropping it's rear end, thereby stepping underneath itself, thereby being able to reach forwards, be it in an upward or extended manner.