A fan never 'cools' a room. It has no way to change the temperature of anything.
A fan does nothing but MOVE air, and air that's MOVing FEELS cooler on human skin than air that's NOT moving, even at the same temperature. Non-living objects, and most animals, don't feel any difference on account of a fan.
It doesn't matter whether the room is open or closed. If the air in the room is moving, then a PERSON in the room will FEEL cooler than if the air is not moving.