I like to remember that the ideal is that if your horse disappeared from under you , would you be able to land in a standing position and stick your landing, like a gymnast doing a dismount? If you were standing, in the position of pretenting to be horseback and posting, than what muscles do you use to rise and fall? Aboard the horse it will be pretty close, except that since the space between your legs is not air, you will be pushing more again this mass, and moving mass, rather than air (in your pretend position) and will generate energy in your rebound off of the horse.
Sorry, I sound like Mr. Science here. One beer with dinner and I'm off and talking . . . . .