Work up to it and like anything else with horse training reward good behavior when it happens. Try shooting at a 3D target with an air rifle, then some subsonic .22s. Try your bow if you have one. Then work up to louder cartridges, and never shoot over the horse's head.
I hunted from horseback as a kid and didn't think twice about taking a shot from the saddle. It seemed deer didn't care if a horse was walking up on them. Peanut would get within 50 yards of a deer, turn sideways and stop, then point out a deer with his ears. Then when he felt me pull the gun out and turn to shoot he'd lower his head to the other side, usually to eat something.
That horse loved hunting as much as any dog. Hunting meant interesting trails with delicious browse, a slow pace, and extra attention. Every shot meant an apple or snack of oats, and he'd jump up into the back of the truck whenever he heard the "H" word (hunting).