It makes sense to close heating and A/C registers when indoor temperature control becomes an issue.
Keep conditioned air out of rooms where you do not need it to keep the rest of the house comfortable and save money by not wasting unwanted heating and cooling.
But, it’s not that simple, as heating, A/C units, and ductwork systems are designed to supply a certain volume of air to each room based on its square footage. One or more registers can affect that careful equilibrium and unintended consequences can occur, as heating and A/C systems do not know whether all registers are open. As long as the temperature control is set, it produces the same amount of heated or cooled air and consumes the same amount of energy. Each room’s supply air volume is controlled by internal dampers inside the branch ducts. It ensures consistent hot and cold temperatures regardless of whether a room is near or far from the unit’s blower. When one or more supply registers are closed, airflow balance and hot and cold temperatures are disrupted and rooms near the blower may acquire too much airflow, while rooms far away may not get enough. The supply registers may be closed to stop airflow, however the return registers remain open. Even without supply air, the return unit draws air out of the room. This discrepancy depressurizes the room and/or section of the house and a depressurized room draws unfiltered freezing or overheated outdoor air into the room through small structural cracks and gaps. This infiltrating air destabilizes room temperature and can degrade air quality. Closing supply vents increases static pressure inside the supply ductwork which in turn stresses the unit’s blower, potentially leading to shorter repair life of that component.