I did all sorts of things with my previous horse. I taught him everything I could, even if I was just learning it myself, haha
I taught him to be ridden with no saddle, bridle, etc, stood on his back, taught him to do a nice sliding reining stop and spin, jumped him..you name it
The only thing I tried on him that was really a bad idea was when I tried to jump him over a little stream crossing over the path I regularly rode him on- on the side of a hill. He jumped it okay the first time, I got lucky, but then he decided not to jump it again (because he's smarter than me) and I flew off and came an inch away from rolling down that hill, but got lucky. Instead I just landed in this huge thorny weed and got thorns stuck all over my bare skin (I was wearing a spaghetti strap tank top), some of which took a month to come out! And I had this big scar across my cheek that stayed there for about a year.
Yeah, that wasn't a smart idea..