Captains perform a useful purpose, with bonuses that affect the troops a noble leads in various ways. But captains take absolutely no effort on the part of the player. You don't have to go hunting for them, you can't buy them or hire them, you don't have to pay them, they take no effort whatsoever on the part of the player. They can be completely ignored by the player, and they will still do their job.
A horse, that every noble in the world probably has multiples of, and would only ever be noticed by another merely by their conspicuous absence, is something that would very little to nothing to the game. Being able to/having to spend hours caring for your horse? Isn't that what grooms/squires are for? And in return you get some kind of traveling bonus for when you don't have a unit to lead? You a;ready get a travel bonus when you're not leading a unit, because you're assumed to be traveling fast and light, because you have horses. Kind of like cavalry units travel faster, because they have horses. If we were to give a horse travel bonus, we'd actually have to slow down everyone who was traveling without a unit and didn't have a horse. And then we have to worry about horses dying, and having to buy new ones, naming our horses, being able to buy multiple horses for multiple benefits, etc. etc.
To be honest, I can't see Tom ever adding any kind of game mechanics to deal with something as mundane as a horse. "Pets" of all kinds are a rejected request. I think that horses would almost certainly fall under the heading of pets.