They are called Horse bows because they are the style of bow traditionally used by horse riding, often nomadic peoples. The Huns, Mongols, etc. They are short compact bows that can be easily draw while riding horseback, although they are also found in the Scythian culture. (think the classic Greek works showing archers. the "heart shaped" bow of Dianna, etc.) Traditionally you will find many (most?) were composite. Made with horn limbs and wood risers and tips. I have seen documentaries where they tested traditionally made long bows against horn bows and found that the horse bows were capable of faster and heavier hitting shots. But that may have something to due with the higher draw weights conbined with the deep recurve shape of the bow.

(all subject to accuracy of my memory)