This is something I've seen instructors doing with little kids, but it helps them get the hang of their body and balance. They have to ride in rising trot without holding onto the reins - it helps stop them from leaning on the reins, but it's also really good for their balance. Once they get the hang of that (the horse is led, obviously), they play Simon Says: touch your nose, put your hands out like an aeroplane, wave your left hand. All in rising trot.
It'd probably be a bit undignified for us grown-ups to do 'around the world', though xD For those who have never encountered it, it's when you have to turn around on your saddle and end up facing back where you started - so yes, you've got to swing your legs over the horse's neck and bum!
If you believe everything you read, better not read.