As a rider it is important to have a horse match to you that is the right size. It is less important for the horse, but for aesthetic reasons most people want a horse that looks appropriate to their body size and type. To find the right sized horse's not simply a formula of relating your height to the horse's height, but is much more complex.
Factors that should be included in figuring the right sized horse are not only your height, but the length of your leg and the length of your upper body, the height of the horse, the build of the horse, and the shape of a rider. How to find the right sized horse's usually best decided by riding many horses and getting a professionals opinion from the perspective of the ground how you look on the horse. Any horse that can safely carry you is the right size! However if you plan to show your horse, or care whether people think, you should find a horse that is suitable to your body. In the show ring suitability of horse to rider is factored into judging and may be the difference between a blue and a red ribbon.
Avoid the temptation to buy a horse that is too large. A horse that is too large can carry you comfortably, but because your legs may not reach far enough around the horses barrel you will have less control over the horse. If the horse you buy is too small, your feet will hang past the bottom of the horses belly and you will find it more difficult to give cues with your leg. To find the right sized horse to buy, you should ride as many horses on trial as you can. Ultimately, though, finding the right size horse comes down to what you are comfortable on!
This horse and rider are well suited to one another. The riders heel reaches the underside of the horse's belly without hanging past it, and the rider's upper body appears to be in proportion to the horse's neck and build.