Instructions
Research "Agriculture." This is a beginning tree for your Civilization, and it will lead to important developments needed for horses.
Research "Animal Husbandry" (unlocked with "Agriculture"). This leads to two new technologies: "Writing" and "Horseback Riding." It also unlocks pastures and horses.
Build a "Stable." If horses are not native to your civilization, purchase horses from another civilization to begin breeding them.
Research the "Horseback Riding" skill (unlocks when you build a stable). You will now be able to train mounted units, such as "Horse Archers" and "Cavalry."