The only horse back riding was for running my trapline 30 yrs ago and I left the rifle home and packed a 22 handgun. Duke wouldn't put up with shooting off his back but if I got off and stood in front of him and he could see the pistol he could care less.
Now I do carry a scabbard on my back when I'm hiking, skiing, bicycling or on the MC chasing coyotes. I tried a scope with tall turrets, what a pain and gave it to my granddaughter.