I don't think there is much you can use that will faze a goat, that wouldn't do damage to your horse. You may consider covering them (the mane and tail) up, maybe that would help. You can braid into a tail bag and use a sleazy hood. But that more than likely is more trouble than it's worth. How do you feel about a roached mane? Then you could still use the tail bag.
The only other thing I can think of that you could spray or rub on that might taste bad is Alum. Mix it with water and rub it into the hair. The stuff tastes horrible. We used it to keep the dogs from chewing at bandages in the past. Have you tried the Bitter Apple Spray? I'm not sure it would be strong enough to deter a goat though. Bitter Apple