See N, you can turn a horse out on a pasture with cheat grass and the horse will be fine. Its hard on cattle because it gets into their eyes, but not horses. When you buy hay in this country ask your hay farmer if there is any cheat grass in the hay. If there is any at all, skip it! Horses will eat it early in the season, but not after it comes to a head.

To kill it, just mow it early in the season. Do not mow it after it heads out. Cheat grass does not like horse manure, so spread you manure on it in the fall and in the spring, you wont have as much. Continue that, and in three years its gone.