Extractor fan in bathroom, intermittent in cold weather?

I doubt the operation of your fan has anything to do with the temperature. It is probably worn out. If it was an inexpensive on in the first place they usually only go for 5 or 6 years. It is not an hard job to replace it and if you do, buy the best you can afford & it will run quietly and move a good amount of air quickly. Do not buy one with fan blades as they do not move much air. The ones with a squirrel cage type fan are by far the best.