Battery and corrosion
First things first — check your battery. You can do that in any auto part store, and usually for free, and they will tell you if you might need to change it. Then, rid your car of corrosion. Disconnect your cables (negative first!) and clean them with a simple solution of hot water and a tablespoon of baking soda. Dip a toothbrush in there and tell corrosion to beat it. Use a dry rag to dry everything off and protect it from future corrosion with a bit of petroleum jelly. When you’re done, reconnect the cables (positive first!).
Belts and hoses
Take a look at your hoses and belts. Look for any signs of fraying, wear, or leaks. Replace if you see any such sign. It should also go without saying that you should check your breaks. Any squeaking or grinding noise? Replace the break immediately! You can’t take any chances with less than optimal breaks when the weather gets icy. Use that chance to make sure you have all the break fluid you need.
Oil and fluids
It’s best to change your oils before temperatures get extreme. If you live in an area where the winter is exceptionally icy, your car’s fluids will keep it from freezing. Your gas is obviously also one of the important fluids in your car. But it can turn to ice in cold winters. So, if you don’t feel like having your tank frozen, make sure to keep it at least half-full.
Your windshield needs its own kind of TLC. Make sure you have all the wiper fluid you need and that your wiper blades have no signs of wear. If they do — chuck them out and get new, sturdy ones.