A small nightlight is not bad. Just don't use something that requires an electrical cord or a very hot heat lamp which may catch fire. If you can use something like a battery operated LED night light which does not produce any heat and if the birds should kick over the light, straw or other material will not catch fire.

The swans possibly stay near the door for three reasons: One, they know that they can hear you and gain immediate exit once you open the door, two, they may see a slight crack of light under the door and seek the light. Third, there may be a little air coming from the door crack which provides them with some ventilation. Do you have straw on the floor for warmth? Do not use anything slippery as they can sustain leg or foot injuries. Do you have ventilation (window that a predator cannot access) that allows air to come into the structure without creating a direct draft or a cold habitat in the winter? The Regal Swan