We do some mounted shooting. One day I took my 1911 out with a snap cap and rode some patterns just to see what is was like. I had three "accidental discharges." That convinced me that I'll never try and carry a loaded 1911 mounted. Or if I do it won't be drawn until I'm afoot!!!
There are several examples over the years of mounted soldiers shooting their own horse. The CMSA rules are pretty strict on proper technique as are the rules at the National Cavalry Competition. I've some international friends who, due to national rules in their home countries, are limited to using Airsoft pistols and revolvers. Even they have reported "accidents" from time to time.
You can shoot off of any horse once. But when working with horses one must always remember that Gravity is not just a Good Idea, it's The Law!!!