HOA covenants trump city ordinances. They are essentially a contract between the HOA and the homeowner. Any provision that is not illegal (such as discrimination based upon race, etc.) is enforceable, regardless of whether the city itself allows it. The HOA can be stricter than the city, but not more lenient. For example, the city can allow chickens, but the HOA does not have to. However, if the city disallows them, the HOA cannot override it. There are a lot of protections in Arizona from HOA abuse that are not present in other states. For example, the HOA cannot prevent you from flying an American flag, having solar panels on your roof, prevent you from having a satellite antenna. They cannot prevent you from parking on a public street, and even parking on an HOA owned street is protected in certain circumstances.