Check your battery. Colder temperatures put more strain on your battery and its ability to start your car. Take a look at your battery for any signs of corrosion on the terminals, the cables and the tray that holds the battery in place. If you see any, clean away the corrosion or replace the corroded item to ensure proper battery operation. Also check the date on your battery. The typical battery lasts about four years, so if yours is older, you may want to consider replacing it or having it load-tested at an auto parts store to see how much life is left.
Check your engine fluids. Checking your coolant levels in winter is just as important as in summer. You should have a 50/50 combination of coolant and distilled water. If you are not sure if your car has the right ratios, you can easily check with a $10 testing kit available at any auto parts store.
Car engine oil flows differently in colder temperatures than it does when it's warm. Depending on your car and how cold it gets, the manufacturer may recommend a different viscosity during winter months. Check your owner's manual to see if the recommendations are different. Also, while it's never a good idea to delay an oil change beyond your manufacturer's recommended mileage intervals, delaying in winter could put increased strain on your engine versus delaying in summer.
Check the wipers and fluid. Fill your windshield washer fluid reservoir with washer fluid instead of water. Windshield washer fluid won't freeze, and therefore will prevent the reservoir from cracking and also will be available when you need it. Replace your wipers if they are more than a year old or show signs of wear or damage. Worn or damaged wipers won't wipe your windshield evenly or effectively, potentially reducing visibility when you need it most.
Check your belts and hoses. Rubber takes a beating in cold temperatures, which can affect all of the belts and hoses in your engine compartment. Again, take a look under the hood, preferably with a bright flashlight, and inspect all the belts and hoses for cracks and other signs of wear. When the engine is cold, touch, push or squeeze the rubber hoses because cracks may not be apparent otherwise. Push or pull the belts to see if they are taut or loose. If you find any cracks, worn items or loose belts, schedule a visit to your mechanic. Then start the car and let it run while you visually inspect the belts and hoses, again looking for signs of wear as well as leakage, which may be in the form of drips or smoke.