You have an external bell called a NOVA 2,it has a design fault and in the cold it chirps all night like that. There is a fix but it means removing the bell stripping out the circuit board and removing a track on the ciruit board.
Not somnething you may want to do. Get it replaced is the best bet.
As you have noticed it is the cold weather that causes this.
First time i`ve heard of someone using a hairdryer, you on a wind up? But it would cure it for a bit I would habve thought.
As before replace it, and thanks for the laugh!
Alarm
December 2010