I have found that fasting helps conquer the cold and get rid of it faster. Also, it seems easier to fast during this time because the appetite is already suppressed due to the illness.

Hey Archus,
Just started my water fast..http://10daywaterfast.wordpress.com/(sorry shameless plug!!). Anyway my mum started a Water Fast with flu and although she felt rotten for 7 days, symptoms cleared up quickly. I suppose it depends on how weak youre feeling. She didnt feel hungry at all for the first 3 days (because of the cold) but remember that all your bodies energies will be geared towards fighting the cold rather than other internal problems. Good luck on whatever you decide to do :)

From everything I have read about fasting, you should always begin fasting anytime you feel unwell.