I was under the impression that a saddle ring was also used when the horse soldier was in a battle. Kind of like a lanyard ring on a "Fighting Pistol", or police lanyard.
I thought it was tied onto the saddle when going into battle so that the firearm could not easily be taken away from the horseman(like a Police lanyard). And since most were single shots the fighter could quickly switch from his firearm to his sword without worrying about loosing his firearm during the fight?? Tom.