When my wife said she wanted a ring I, being the good and loving guy that I am, bought her a nice 1911 Model 1892 Saddle Ring Carbine in 44WCF....
I had to feign offense when she asked where the ring was and I pointed out the saddle ring. Theoretically I got just what she asked for, except its tied to a nice 1892.
So that's what a saddle ring is for
Contrary to common belief, the saddle ring doesn't tie the rifle to the saddle, but to the rider. Ensuring that no matter where the rider goes, the rifle stays with him. Cavalry riders used to use a leather sling of sorts which they just clipped to the rifle a la Spencer carbines etc. The Winchester saddle rings were intended for the same sort of thing. Its like an 'old school' AR15 tactical sling.