The carrier system used in the Henry, 1866 Winchester and 1873 Winchester simply does not allow the gun to be used as a repeater with a cartridge shorter or longer than the standard.* The case length can vary, but the cartridge OAL must be within specs.
The .44 Short RF was used mainly in small revolvers and pocket pistols, though some would also accept the longer .44 Henry. One could use the .44 Short in a Winchester '66 or Henry, but only as a manually fed single shot rifle, something that desperate people certainly would do if necessary.
* Those rifles have no cartridge stop. If the cartridge is too long, the carrier cannot move upward; it is blocked by the bullet protruding into the magazine. If the cartridge is too short it will allow the next round to protrude into the carrier, also blocking it. While later Winchester carriers can be altered or replaced, the carrier length on the older guns is set by the frame.