I don't know if they're actually prohibited here in my metro Atlanta suburban community, but no one dries their laundry outside. If clothes lines are, in fact, prohibited, then it's almost certainly by our HOA and not by local/state law.
The situation overseas, though, seems quite the opposite. When DW and I were in India recently, absolutely everyone dries their clothes outdoors. Even people living in fancy, high-rise apartment buildings. So much so that virtually every single residential building is coated with unsightly black mold stains caused by decades of wet laundry drippings running down the sides of the buildings. It's quite the eyesore, IMHO.