I ride and bugle to locate bulls. My horse got used to it pretty fast. Right before I let one fly I make a quiet noise first so he knows what's coming.
A good horse will find out pretty fast it's just stupid noises that humans make sometimes. Mine's also fairly accepting of me shooting my .22 pistol from the saddle. He's not fond of my larger guns. I think you'd just get the one chance with them.
On Sunday we were dragging the pack beasts around some local logging company land to get some wind through them and we ran into a black bear. It was the first time for my wife an I to see one while mounted and he was only 50 yards away. The horses and the mule could care less. We rode right over where he'd crossed the road and we could hear the brush popping up where he was moving on the hill side and they didn't seem any more interested than if we'd seen a deer.
Some horses aren't so mellow around bear. At least that's what I've heard.