Training and working with horses involves all kinds of equipment - including a bit and bridle. One question often asked is - why do we need this? Why don't we just train them to voice the way we do dogs?
Answer: Dogs and horses have a key difference.
Dogs have a dedicated part of the brain for understanding vocal communication. Horses don't. This is reflected in the fact that you can't change an adult dog's name - the dog won't cooperate. You can change a horse's name. They don't care.
It is very easy to teach a dog to come when called or whistled. It is possible to teach this to a horse, but it's a lot harder, and some of them never get it. Natural verbal/vocal signals in horses are pretty much limited to "I'm here, where are you" and "Hi." Domestic horses may also vocalize in order to get the attention of humans, having worked out that it's effective.
Horses are trained using some very simple verbal commands, especially draft horses. "Whoah" or "Ho" is a universal that I've heard used by speakers of all different languages. Teamsters use "Gee" and "Haw" to turn. And some school horses learn the names of the gaits and respond to them. They aren't incapable of understanding verbal communication. But while an intelligent dog can develop a working vocabulary of 2-300 words, I have yet to encounter a horse that could understand more than a dozen - Whoah, Walk On, Trot, Can-ter, Gee, Haw and perhaps their name.
So, right, that means dogs are smarter?
Not at all. I'm looking, right now, at the current Grand Prix dressage test. It contains about 30 different actions the horse is requested to take by the rider. That's thirty "words" just to do that one test, and the horse already knows a bunch of actions that are done only at lower levels. On top of that, a trained dressage horse knows a lot of "fine tuning" like "would you please lower your head a touch" or "step under yourself with the right hind a little more."
On top of that, horses have a rich social life with friendships, enmity, socialization.
The thing is - they are simply not verbal. All of a horse's natural communication except for a few signals for when they get out of sight of each other is based off of body language and touch. A horse can't understand what you're saying to him, but he knows what kind of mood you're in right away. (And they distinguish sounds very well - I once worked at a barn that had 60-70 head of ponies that mostly ran out on 80 acres. When the vet's car pulled up, every one of those ponies was in the far end of the field within, oh, seconds. And only the vet's car...)
But because horses are non-verbal, they're often thought of as less intelligent than dogs. I don't think that's true.
For world-building purposes, maybe somebody has bred a breed of horse that's more verbal than others? There are certainly ways to explain a culture that trains horses to voice alone, but it wouldn't be normal.