There are different ways to record yourself while riding a horse. The easiest is to use your phone. Simply propping up your phone is the most affordable way of filming your riding adventures. New smartphones have in general pretty good cameras that will serve this purpose just fine. You can improve the quality of your videos by using tripod. Another option is to use an action camera. You can attach it to your riding helmet on even on your horse's tack, depending what angles you want to catch and what you want to have in focus. When you are riding with a helmet mounted camera, you will have a wider view and better focus. The main disadvantage of this method is that you cannot record yourself and your horse together. The best and unfortunately the most expensive way is to invest in a motion tracking camera. They are very expensive but they are capable of capturing your riding experience in a cinematic way.