Up through the Model 1866 (aka M1867, due to the unique lockplate marking) version, US Cadet rifles were miniaturized versions of the service rifle. Beginning with the Model 1869, they were made 3" shorter, but not otherwise scaled down.
The "Model 1866 Rifle, Short" came about as the result of muzzle damage found on about 1000 stored full-length rifles. This 'repair' process was confined to the M1866. No other model was so modified, though some 1800 Model 1884 Rifles were converted to Cadets, in 1895, and perhaps more later.