This is not legal advice but in California, the landlord of a rooming house (which it sounds like you are in) has the right to make reasonable house rules and “keep the windows closed when the AC is on” is generally recognized as reasonable rule. Its unlikely a court would side with you on this.

Keeping the window open in a room (even with the door shut) impacts the temperature and humidity of the rest of the house. Rooms within a house are not air tight when the door is closed. In fact, the airflow in a house is designed to circulate and mix all the air from all the rooms so that the AC runs efficiently, even when the doors are closed.