I have taken horseback riding lessons; and the teacher I studied with who also owned the horses instructed us to use our bodies to communicate with the horse. For example, when you want the horse to speed up first you sit forward on the saddle and squeeze your legs together, against the horse's side. In addition, you slacken the reins. To slow down, you just do the opposite. You sit back on the saddle and relax your leg muscles, and be careful not to touch the side of the horse with your heels. You also tighten the reins.This is also referred to as "sitting the trot" at first it feels really bumpy but the horse will get the message and then slow down.
If you practice riding bareback, these techniques become more obvious, since the horse can feel your body tightening and relaxing more easily.