The best adivice for driving in bad weather is not to drive at all, if you can avoid it. At the very least, wait until the snow plows and sanding trucks have have a chance to do their work, and allow extra time to reach your destination.
Bad hoses, belts, water pumps, spark plug wires and distributor caps can leave you stranded in the winter. It's better to spend the money now rather than after you've been stuck in your stalled car in freezing weather!
An old battery can leave you stranded because it's old! If you need a new battery, choose the biggest battery your car will allow. It takes more power to turn over an engine in cold weather because oil becomes thicker in cold weather. Also, batteries lose power as the temperature drops, so you will need more power to start the engine from a battery that produces less power in cold weather.
Most areas need a 50-50 mix of antifreeze and water to protect the engine in cold weather. Note: 100% coolant has a higher freezing point and lower boiling point than the 50-50 mix - so, don't use straight antifreeze.
Antifreeze isn't just about protecting your engine, it's other purpose is to keep the cooling system from rusting. The rust inhibitors break down over time and need to be renewed. At a minimum, change the antifreeze at the interval recommended by the manufacturer.
Take care of any leaks in the cooling system, too. Cars with low or no coolant can overheat, even in the winter time. Overheating can cause expensive engine damage whenever it happens, and when if you have no or low coolant, you have no heat!
Be sure the wipers clean the windshield well, and that you can see clearly in wet weather. When using wipers in the winter, turn them off BEFORE shutting off the engine to avoid having them freeze to the windshield. This will also avoid burining up the wiper motor because it's trying to put the wipers back into the rest position.
If you become stranded or stuck in the winter, the engine is your only source of heat. You can run the engine indefinitely at idle, at no danger to the engine, to stay warm -- that is, as long as you have gas. If you have an older car, you might want to crack a window to avoid carbon monoxide leaking into the car from rust holes or exhaust leaks. If you are stranded in a blowing snowstorm, remember to get out periodically and remove snow from around the tail pipe to keep it unobstructed, and to avoid carbon monoxide poisoning.
You can easily go through a half gallon of windshield wiper fluid on a messy day trying to keep the winshield clear. For this reason, it is a good idea to keep some extra fluid in the trunk in case you run out. Try to buy the "good stuff." Cheaper fluid may say "Good to Minus 30," but it may freeze at 0 degrees.
Every car has different handling characteristics. You should know what your car can and cannot do in the snow. You should know if you have front wheel or rear wheel drive, part-time or full-time four-wheel-drive, antilock brakes, traction control or stability control, and what kind of tires are on the car. You should know how all of those things work and how they do and do not help you in snowy or icy weather.
Invest in a substantial snowbrush and ice scraper. It's also a good idea to have a shovel and a bag of sand to help with traction, and of course, extra windshield washer fluid. It's also a good idea to have a blanket in the trunk, along with some extra winter clothes and a pair of boots.
In other words, make sure that you have good visibility. Clean off the entire car, not just a little peephole in the windshield. You will need MORE visibility in poor conditions in order to drive defensively. Make sure every glass surface is clear and transparent by using a snowbrush and ice scraper. The side-view mirrors and all the lights should be brushed and cleared as well. While you're at it, clean the snow off the rest of the car so snow doesn't slide off the roof and cover the windshield as you slow down, or fly off on to someone else's windshield, maybe causing them to run into you.