"Getting back on topic.". It's a seamless web here, 79.
Right hand cross draw is how I roll. That's always worked best for me, especially with 7.5 and 8" barrels. For regular concealed carry I use a Combat Commander on the right, conventionally.
I used to breed American Quarter Horses and took care to 'bomb proof' any that were for trail use. As to gun choice: Plow Handle Sixties were made for shooting horseback. No better handgun for that.
I let my mare, Hell-Bitch (not it's registered name), see the pistol and hear it cock before shooting the first time. No surprises. After that she's good for the day.