The type of grass you need to grow to feed your horses depends on where you live. The United States is divided into 3 zones, as far as lawns are concerned -- warm, transitional and cool -- and picking the right type of grass will give your horse plenty of food.
If you live in a horse-mad state like Kentucky, choosing Kentucky blue grass is the obvious answer. This cool-season grass endears itself to people and horses alike. One of the first grasses brought to the United States, this vivid, greenish-blue, fine-bladed grass grows into a dense turf and is cold resistant. This makes it ideal for pastureland; horses love it, whether they're eating it, racing on it or just playing.
Another type of fine, narrow-bladed grass to consider is the newer varieties of perennial rye grasses, which stand up to heavy wear and tear. Suitable for wet, heavy soils in temperate areas these grasses establish themselves quickly and produce a dense mat. Of course, horses don't care what your lawn looks like, they only care about the taste and how easy it is to roll on and gallop on; they're big fans of perennial rye grass.
As you don't need to worry about having a perfect green lawn if you keep horses, choosing a native North American plains grass, like buffalo grass, could be the answer if you live in a dry area. However, an even better solution would be to put together a good lawn mix that will allow you to please your horses as well as your family. Combine a fine lawn grass, like bent grass, with several sturdy grasses, like carpet grass or St. Augustine grass, and throw some blue grass into the mix, as well. After a while, you should have a lawn that will look good and taste good, too.