Pack your car with a few essentials to make sure you're prepared for any situation. Get a box and fill it with some warm and waterproof clothes, some heavy boots, thick gloves and socks and rugs or blankets. Take a sleeping bag too, if you've got one. It's not unheard of to be stuck in the car overnight in nasty weather conditions and you'll be thankful for warm gear if you do. Add a torch, an ice scraper and your phone charger while you're at it, and some food too - chocolate bars and non-perishable goods. Don't forget liquids, and if you're super prepared take a flask with some warm drinks or soup in it.
While you're at it put a brush, a shovel and a hi-visibility jacket in the boot, and keep the fuel tank filled up - your engine is your means of keeping the car's interior warm and lit if you get stuck and it's no use if you run out of fuel.