Frozen door locks : keep a small bottle of lock de-icer in your pocket.

Tires: Mud & Snow tires are not necessarily ice tires. All- season tires are definitely not for winter. Check this article : http://www.canadiandriver.com/articles/jk/at_011101.htm

Windshield washer liquid : get the -20°F type

Windows fogging inside : Keep the car floor as dry as possible and crack the windows at all time.