Think of horses like dogs with a vast array of breeds and temperaments.

There are breeds and varieties of horse that are more or less sensitive/excitable. That’s why we refer to some as “hot bloods”, “warm bloods” and “cool bloods”. Race horses like arabians or thoroughbreds fall in the hot blooded category. They’re sensitive and excitable—that’s why they’re good at running fast on command—it’s prey/flight behavior. Draft horses like clydesdales fall in to the cool blood category. They’re very big and calm and stable and good for work. Warmbloods are prolific in dressage, which is based on military riding disciplines. You want them a little fast and flighty, but also a little calm and collected. They can often be big, too, because they were bred to carry knights and artillery into battle (edit: i may actually be thinking of cool bloods that were bred to make modern warmbloods, but i digress).

War horses are going to come from less temperamental hot-blooded breeds. From there, you also have a very very social animal that can be bonded to a rider and trained for certain jobs. Horses are herd animals and adept at working as a unit/following a leader. Instinctually, some horses know that sticking out from the crowd is deadly.