A leather strap was run through the "saddle ring", tied, and then the strap could be hung around the saddle horn. The rifle was very handy for the rider.
The U.S. Cavalry used the ring on the Springfield .45-70 carbines, with a belt-and-hook attachement, to have the rifle hanging from the trooper's shoulder.
Later, the rifles were sometimes carried in sewn together leather "funnel-like" pieces, straped to the pommel, with the rifle horizontal, just in front of the rider's crotch.
This then led to the many variations of the saddle scabbard.
There may well have been other uses, but those are the ones of which I've read.
J.B.
