Don't know why I got thinking of this today, but I thought back over the goats I have had over the past years.
Must be 35 years ago (eek, that long!!) I acquired a goat kid to bottle feed from a neighbour. He had bought a milking toggie - and went out one evening and it had a surprise female kid. He had milked her that morning, quite oblivious to the fact she was in kid. Tanya, the kid, never had horns. And Penny, a British Alpine was polled. I remember taking her two kids to the vets and him commenting on the fact the kids had no horns, which he found rather unusual.
Her subsequent kids, were all polled.
I have it in the back of my mind that apparantly polled goats are none breeders - not sure if this applies to cows etc. too. Penny bred ok, but come to think of it, one of her daughters, a very large girl called Heidi, was polled, and we never managed to breed from her.
Never seen any polled goats for years.