According to the Speer reloading manual;
"In the late 1800's, it was both prudent and fashonable to pack a revolver and rifle chambered for the same cartridge. Winchester developed a trio of rifle cartridges - the 32-20, 38-40, and 44-40, that were picked up by Colt for its famous Single Action Army revolver.
Both Colt and Smith & Wesson chambered revolvers for the 32-20 cartridge until WWII. In addition to the Single Action Army, Colt produced double action models in both their medium and small framed actions. Smith & Wesson chambered their Military & Police model (the forerunner to the Model 10) in 32-20, but the 38 Special became so pervasive by then that the smaller 32-20 was dropped."
Being weaker than a 38 Special, I'm thinking it probably shouldn't be used on game any larger than a coyote.