I would endorse the diagnosis and advice given above.
It may be that your battery is on its last legs - cold weather is hard on batteries and exposes the weak.
A convenient battery conditioner is what you need (no need to open bonnet etc) - here is a link to the UK site that markets such a product http://www.racecar.co.uk/airflow/
, I feel sure there must be a supplier in your neck of the woods. It will still be useful even when you have a new battery and do 12 mile trips in ccccold weather!!!