Growing up in the Chicago area, I've always expected to get stuck in snow at least once per winter. Now city driving is a bit different from suburban winter driving, but I still like to be prepared for whatever winter might throw at me. This is especially true if you live in a more rural area or travel a lot (like for Thanksgiving or Christmas!). Caring for your car will always be worth it. Best thing is you shouldn't have to buy a lot to be prepared for winter - most of this stuff you have, you just need to make a point to put it in your car!
First you'll need to prepare your car for winter. Get your oil changed on time & get your battery tested (my car is currently dead outside while I write this - not a good situation you want to be in when it's friggin cold out). Fill up your windshield wiper fluid and if you can change your tires to winter tires. Winter tires are absolutely worth the money, in my opinion. Two-wheel-drive cars with snow tires typically out-perform Four-wheel-drive cars with all-season tires. Winter tires are designed with a softer, more grippy rubber that keep you from skiing in your car when the all season rubber freezes up (possibly saving you from a collision), and they feature treads that help grip as well. If you have sub-freezing temps and any precipitation, look into it.
There are some things you should keep in your car year round. A water bottle & a (non-melty) snack are good to keep, plus a towel, small first aid kit, a flashlight with batteries, jumper cables, and a cell phone charger. As Douglas Adams says, "A towel, [The Hitchhiker's Guide to the Galaxy] says, is about the most massively useful thing an interstellar hitchhiker can have". Use it for downpours, pets, to keep furniture from scratching, as well as a blanket and for cleaning off the car in winter.
When cold weather comes around you should keep some extra goodies in your car. Keep an extra set of gloves, a scarf, & hat in your glove compartment. I moved my extra car manuals to my jumper cable bag so I have extra room (I mean, if I need those, the car's going to be stopped, so why take up valuable glove compartment room). Also hand warmers, anti-freeze, kitty litter or sand for traction (or salt if you aren't near a body of water, but in most areas salt is hurting the ecosystem, so a natural kitty litter is best), blanket, small shovel (get a fold up one that you can just leave in the trunk), & brush & scraper. You probably carry most of these already if you live in a cold climate.
Now if you travel during cold weather, you'll need a bit extra. Consider a Swiss army knife for the glove compartment, flares or an LED emergency light, an extra pair of winter socks, and water bottles in a cooler (the cooler will keep them warmer than the outside temp - maybe even put a hot water bottle in there). Maybe get an extra cell phone power supply. If you're not wearing them, bring along your winter boots & jacket, and be sure everyone in the car has a set of gloves/hat/scarf.
Now the super-safe list. These are things for long winter trips or if you're in very rural areas - basically if it might be a while until someone can help you out. Some people bring candles and matches, but how effective they are vs. the possible danger is debatable. Definitely bring extra flashlights & batteries. Also heavy duty winter boots (like Sorel), a sleeping bag or a bunch extra blankets, a whole extra set of clothes that can be worn over your clothes, mylar space blankets, and a ski mask. Also bring extra food & water - possibly enough for 24-48 hours. Definitely bring a high power LED emergency light with extra batteries. There are options for an emergency heater, but as I don't know much about them, I didn't feel comfortable recommending one. If you're in an area that you might need one, I guarantee you can go to your local hardware or outside goods store and they can help.
I wanted to add in a little extra list: If you park outside in winter, you need your goods both in & outside your car (for when you can't get to your car just yet - yeah, it happens). Like, if any of you remember that blizzard the night of the SuperBowl? I walked outside the next day and my sedan was 75% covered by snow. Took 30 minutes of shoveling to just open one door to access my brush & scraper. So yeah, you need stuff outside your car.
Inside your car keep a small shovel, your brush/scraper, a pair of gloves (preferably waterproof), kitty litter and anti-freeze. Outside your car keep a shovel of any size (if you live in an apartment, the building may have one you can use), gloves, an extra scraper, and something to get snow off the top of your car if you can't reach, like a hockey stick or a long, sturdy brush. You can also use a spray bottle filled with 2 parts isopropyl alcohol (or even just crappy high-percentage vodka) & 1 part water to help defrost your windshield & car handles, though I've never tried it myself. Or 3 parts vinegar & 1 part water - don't leave it on the body, though, as vinegar is acidic and will etch the paint.
What do you keep in your car in winter? Any suggestions for winter driving?