Perhaps the single most important piece of advice I’d like to offer you when it comes to writing horses is this: don’t rely on terminology. Terminology is a trap.
There are plenty of occasions where a judicious application of technobabble will get you through, even when you’re completely making it up as you go along. Advice for writing horses often boils down to this, too — “whatever you do, just use the right words and you’ll be fine!” — but when it comes to horsemanship, throwing around terminology can be a particularly risky proposition, especially if you’re writing in anything but a modern-day setting.