The horsepower you need depends on how fast you want to dig. - But you really don't want to dig fast.
With any auger, and with most any tractor, there's always the risk of corkscrewing the auger into the ground to the point the tractor doesn't have the 3pth capacity to lift it out. So with all augers you take small bites, raising it up and down often to clean itself off before reinserting.
Bottom line: (IMHO) you don't need much horsepower to turn an auger if your going slow enough so that you don't overfeed it beyond the tractor's capability to lift it out. Think about the little handheld gas powered one-man or two-man augers. Granted, they're not 12" but there's really not much torque there if one 180 lb man can hold it in place. ....and that's my 2 cents.