No.  A Homeowner’s Association (HOA) cannot enact rules that prohibit children from playing outside. This would be illegal.  This is true even if the tenant is not an owner of a unit at the complex, but merely a renter.  Condominium Associations do not have special status over apartment complexes. They don’t get to make their own rules, simply because they own the place.  Fair Housing laws apply to all housing, not just apartment complexes.  HOA’s are not immune from Fair Housing laws.  Fair Housing laws prohibit HOA’s from materially restricting the children of renters and children of owners from playing outside.  Any rule enacted by an HOA that materially interferes with children from playing outside is illegal.