Funny how we're told the .30 Carbine won't work on deer, but the 32-20 has been used as such for almost 140 years, (Elmer Keith used a 32-20 revolver to take three mule deer and an elk (SIXGUNS pp.276)) and now the .327 Federal, either from a revolver or a Henry lever is said to be the berries for deer. Either of the aforementioned are less powerful than the .30 Carbine from a rifle.
I say, as with any cartridge, place your shots properly, go forth with a good bullet and load, and you'll be fine.
