Claws aren't a weapon. Teeth aren't weapons. Neither are they unarmed strikes.
There isn't an exact specification for a natural weapon in 5e, but they aren't weapons and they aren't unarmed.
Except when they are, like the Tabaxi. If anything, the horns would be treated similarly, as this creates precedence. But that feeds right into my point. One UA says a natural weapon is a weapon. One official race within the RAW treats its natural weapon as an unarmed strike.
UA is not RAW, and if this ever becomes official, the horns will not be weapons.