The sound that a horse makes is called a neigh. A horse's happy neigh is sometimes a greeting to other horses.
You can use neigh to talk about the noise your horse makes, also known as a whinny or a bray. Neigh is also a verb: horses neigh cheerfully or in frustration, and your little brother might like to ride a broomstick wildly around the house and neigh. The word comes from the Old English hnægan, which is most likely imitative of the actual sound of a neigh. In other words, it's an example of onomatopoeia — when a word sounds like what it means.