As people say they will desensitize but you can make it a less stressful proccess.
Well if your patient and take some time it's doable,horses and wildlife do acclimatize to gunfire.My local range has to call ceasefires when deer wander onto a hot range. We physical have to go out and chase them as gunshots/bear bangers have no effect.
There isn't one single solution ,start with placement of range and direction one fires. Firing from inside an open sided shelter with the back towards the pasture is most ideal. As a musician try get some sound absorbing/deadening panels to use on the shack
Along with the backstop berm, a berm between range and horses, adding trees bushes helps absorb some sound. Ideally your trying to reduce the sharpness of bang rather then loudness.
Even if you can't do everything all is not lost. Start by using .22s and while someone is shooting(slow fire) have person by paddock with food/treats. The ideal spot is the point furthest from range as this is where horses will go to. While skittish at first possible, if you don't appear concern and there is food that goes along way. In a perfect world if you can have a horse that's 'bomb proof' start with them then slowly add other horses, horses will take cues from other horses as to the 'danger'
Another trick is to also pre-warn the horses that shooting will commence, horses flight animal and their instinct is to run first then after a bit stop and if no danger they stop and eat. Hooking up a buzzer near the paddock(doesn't have to be loud) that you can activate from the firing line just prior to commencing shooting.Realistically this one is a bit overkill.
Start slowly, observe and go from there. It is doable