Brakes - Check them. Your pads could be worn, your rotors cracked or warped, and your calipers weak.
Tires - Winter isn't a good time to have bald tires. If yours are smooth, get new ones. If yours are fine, make sure they're properly inflated and rotate them to extend their life.
Battery - Open the hood and look at it. If you see weird and chalky growth formation, clean the connections. If your ride has a hard time starting, consider replacing your battery since summer heat does the most damage to battery life and is why they often fail in the winter.
Wiper Blades - You can't drive well if you can't see the road. If they aren't doing a good job with the rain, they're definitely not going to do well with sleet, snow, salt and dirt. An all-purpose wiper will normally do the job, but for those living in regions with an extra helping of winter, buy a higher priced winter wiper.
Shocks and Struts - If you dread potholes, have unusually bouncy wheels, or just want to go slow and low, consider replacing your worn out struts.
Engine Oil - Viscosity matters. Fortunately, you don't need to know what that means. Just stay current on oil changes.
Other Fluids - Top off your fluids. Or have someone else do it for you. This includes coolant, brakes, transmission, power steering, and windshield fluid.
Engines - Does your engine sound strange? If it's bad in the summer months it's going to get worse in the winter and that's not the time to break down. Get it checked out now.
Belts and Hoses - Worn, cracked, or frayed belts and hoses can lead to more expensive problems, like engine failure.
Air Filter - These are like surgical masks, filtering out harmful stuff. If your filter is dirty or clogged, get a new one.
Headlamps and Tail Lamps - You want to see and be seen. Start your car. Place the transmission in park, or neutral and pull the emergency brake. Turn on lights. Walk around the vehicle to ensure they work. Do the same for the brake lights.
Bottom Line - The problem with maintenance is that we pay money and what we get back is the same thing we had before. Our car isn't any more luxurious with a new air filter, but we're stuck paying the bill. Much like insurance, we pay for maintenance because we know that in the end, it will save us a lot of money by making our car last longer.