While sadly not a real working one i decided to crate a barber shop in hammerdeath bungerlow, it is owned by my redguard so its design has elements blended into it.
Can be viewed on PC NA
I, for the life of my cant understand why we do not have a barber shop in game. Its a good way to help sink gold out of the game. ZOS could also create a barber shop chair that is sold for crowns that people can use in their homes, or do like you did and make a legit barber shop.