First and foremost, the anti-freeze, the windshield scraper and the winter windshield washer fluid. You can't drive without them, you can't even start the car without them. Replace the old anti-freeze, in case you have one, with newer liquid, and don't forget to change the summer windshield washer fluid with the winter counterpart that contains special cold-resistant substances. The windshield scraper could prove to be extremely useful in case you want to remove frost, ice or snow from the windshield. The latest car models are equipped with special defrosting and heating system which may replace the traditional scraper, often regarded as a risky tool that may scratch the window.
Secondly, the tires. The tires are extremely important because the winter versions are especially designed to be used at lower temperatures than the all-season variants. The winter tires provide a better grip combined with increased handling and could stop the car much faster than the summer ones. However, don't forget to check the pressure of the tires (it is said that the tires' pressure is altered every time the temperature raises or drops with 5 degrees). Although you're recommended to use winter tires on all four wheels, some people choose to install them on only two wheels, on the front or on the rear, depending on their traction control system. However, if the winter tires are a little bit too expensive, you can always acquire a set of tire chains that should help you in case of extreme snow conditions.
Next stop, the battery. Don't forget to check the battery, it has quite a tough life during winter so, if it's very used or happened to cease in the past, you'd better replace it with a newer one. Also, check the terminals, the wires and the other connections to be clean and without any sign of rust. Jumper cables are also recommended, just to be on the safe side.
After the battery, the engine is the second component to duel with the cold weather. Although checking some parts of the engine, including the hoses, the spark plugs and the driving belts, could sound like piece of cake for some experienced drivers, you'd better leave this job to an expert. And if you really decide to go the service centre, you're also advised to check the brakes. In fact, the main braking malfunction during cold seasons is a faulty synchronization which may cause the car to slide sideways.
And because we're sure you'd like to drive the car during winter wearing a T-shirt, don't forget to verify the heating, the defrosting (if available) and the de-fogging systems because they all have a pretty tough time during cold seasons.
Although the car seems to be ready for winter, let's get to more paranoiac stuff. What if you get stuck in snow near a forest or the car runs out of gas in the desert? (OK, maybe this is a bit too extreme, but you know what we mean) Well, in this case a mobile phone may save your life but if you want to get out of this situation by your own, you'd need a bag of sand, a shovel, a flashlight, a first aid kit and why not, a box of matches. And in case you can't turn on the engine, you may take in consideration using the blankets, the winter shoes or maybe another jacket or pair of pants.
Well, that should do it. However, don't forget that driving responsibly and with extra care during the cold season may simply turn all the above safety measures into pure waste of time.