There are other very good reasons to close your balcony door.
Ship's ventilation systems are designed to save your life in case of fire.
The system maintains a higher air pressure inside your cabin than in the corridors. In case of fire, the over-pressure blows smoke and flames away from your cabin, rather than into it.
If you leave your balcony door open, that over-pressure dissapates outdoors. Then the A/C system tries to build pressure in your cabin by robbing the air from your neighbors' cabins.
If your neighbors are smokers, you get their smoke.
Whether or not they smoke, you get their cold air.
They complain that the A/C is not working.
If there is a fire, you are all in trouble.
Please read the sign on your balcony door, instructing you to keep it closed.