I think it may depend on how you carry your rifle. I have read that 19th century cavalrymen typically carried their carbines muzzle-down. When the Army adopted the Minie system, they did indeed find that the bullets moved, and they were well aware of the consequences.
As discussed in another thread a while back, there are several period paintings showing mountain men and plainsmen with a spare rod carried in the bore of the rifle. I suppose this was a logical, safe place to carry a fragile and necessary bit of equipment, but the rod may have helped keep the ball seated. At the very least, you could judge the position of the ball by the amount the rod protruded, and reseat the ball, if needed, before shooting. When the rod was removed, it could be used as a monopod rest for the rifle. That is documented, too.
I have no personal experience carrying a muzzleloader on horseback. Considering that 19th century military Minie bullets are typically sized very slightly (.001"-.002") under bore size, they could easily drift some if the rifle is carried or jostled with the muzzle down. I would think a patched round ball would fit more snugly and would be less prone to move, although I suppose it would be possible.
Best regards,
Notchy Bob