I talk a lot during lessons about the importance of a steady rhythm at all gaits. A rhythmic walk, trot and canter are not only more comfortable to ride but they are one of the most very basic keys to having a relaxed and supple horse underneath you who is capable of fun, higher level stuff in any discipline.
Some horses, like our Calypso, seem to have an internal metronome and need very little from their rider to help them maintain a perfect rhythm. Other horses, like Clay and Tia, tend to speed up as they go–especially when they lose their balance, like during circles or whilst changing rein–unless their rider is actively half-halting and re-balancing them.
In this video, you'll see me demonstrating exactly that...every time Clay speeds up, he either receives a half-halt or I transition to the walk or halt. There is a little lateral work now and again to remind him to stay in my outside rein and maintain a nice inside bend. We have a lot of work to do still, but since this video was taken (in August), I'm happy to say that our rhythm as improved a lot and he is more relaxed and "unlocked" through his back than ever before!
So, rhythm can be taught! With patience, time, a million half-halts, and the occasional downward transition when they really start rushing. The goal is to keep the horse's weight rocked back on their hind-end as much as possible. When they get heavy on the forehand (you'll feel it in your hands when they lean on you), that's when they'll want to rush. Throw in a transition there, to rock their weight back again, but be careful to ride the transition correctly (don't just pull on your horse's mouth) or they'll become defensive and even more tense.
With every ride, remember: don't shoot for perfection–reward the "try" in your horse or they will get frustrated and resentful. At the same time, don't accept anything other than their best effort. Otherwise you're just rewarding them for avoiding hard work. This requires you to really know your horse. For instance, last week Clay's best effort was completely different than this week's. He has progressed a lot in one week and I now expect better things from him than I did a week ago.
Working through some of these nit-picky things can be unexpectedly challenging for many horses, so try to keep it positive for both of you for the best progress.