Does it hurt them to have other people get on my horses?

BILL— It can be good or it can be bad pending on a lot of factors, namely what the riders are like and the temperament and level of training of the horse in question. The first thing to resolve is your motivation. Is this to benefit you, the other rider, or the horse?
One of the most memorable rides in my life was in December 1974 when one evening at the Poulins’ I was invited to have a short ride on a Hanoverian mare who had been the reserve horse on the Canadian team at the Munich Olympics. It was all carefully supervised of course, but it did great things for my self esteem as well as giving me a new, very meaningful reference point.
It’s a great gift to be able to bestow on someone if you have a special horse that they can learn from. That said, the most important quality that a rider must possess to be allowed to ride your horse(s) is judgment – knowing what she is capable of and what she should leave alone.
If it’s a question of allowing a person more knowledgeable than yourself to get on your horse, their judgment and your trust in them are still the operant qualities. From my personal viewpoint I feel that anyone who rides with me should-– if I deem it useful– be willing to let me on their horse. I think I know enough at this point in my career not to bite off a lump I can’t chew!
I can think of several examples, however, where a rider did not want a particular clinician climbing on their horse to show off in a way that could be detrimental to his ultimate training. That is a difficult circumstance! On the other hand, If the owner knows the horse has some dangerous behavior that hides under the surface and does not want anyone else getting on, that is understandable.
Ruling out such instances, by and large it is not only valuable to get on other people‘s horses but also to see a more advanced rider working yours. Sometimes a new slant on an old problem works wonders.

The other consideration is if your horse is in an especially vulnerable stage of development. At various times “one voice” is all a horse is able to deal with, and more than one is just confusing to him.
The thing to remember is that for good or bad, anytime anyone gets on a horse he/she is training it. Deciphering what sort of experience he’ll have allows you to decide if the only boots that should go in your stirrups are yours.
One last thought – if the reason you want no one else ever on your horse is that you want to do it all yourself, that’s just vanity. Get over it!