It always depends on horse. Noone is getting on my paint, and I'm happy if my trainer rides my qh, but she does it very rarely. I'm not jealous about other people messing with my horses, but I do NOT trust my horses to be ridden by other people (I had a bad experience in past).
My qh is surprisingly good with my current trainer, and I actually let my visiting aunt (who never been on horse) to get on her to take some pics, and they both did great. But she didn't ride her per say.