First of all, you're gonna want to make sure you have a spare tire. That is car smarts 101. And if you don't have a spare tire and don't want to spend a ton of monies getting one, try to find a used tire shop. You can usually find a good tire for a better price.
Step 1: More Car Smarts
It might be a good idea to have a few tools in your trunk along with your tire. You will of course need a tire jack, but a wrench and some screwdrivers are always good to have. Also, a flash light and backup batteries are a must. And don't forget your shovel. Please. It's just common sense.
Step 2: The Kit of Aid First
Now that you've got those things taken care of, we can move on to survival style stuff. You will need to either put together a first aid kit or buy a cheap one at your local pharmacy.
Step 3: Warmth
YOU WILL NEED TO STAY WARM!!!! Picture this, it is winter, and you have to shut your car off. You only have one jacket and it's probably flimsy. How will you keep from freezing your face off? Oh, right, the handy dandy trunk kit must have a blanket. In case that wasn't clear enough, put a blanket in your winter kit!! You may want to put more than one blanket just in case you have a passenger. Gloves are also a smart thing to put in your kit. They will keep you from getting frostbite.
Step 4: FOOD!!
Ah, the most important part. Food! We've already taken precautions for keeping you safe from the cold, so it wouldn't do to starve to death. Pack some yummies, like maybe some beef jerky or peanuts or delicious gummies. Basically anything that you find tasty and that will last for awhile and not rot in your trunk. And of course, water. Water is pretty cheap, so go ahead and buy a whole case. You will regret it if you don't.
Step 5: Icy Stuff
Here is the last thing that I can think of. Often in icy and snowy conditions, cars can get trapped in the snow drifts. What you can do is keep a bag of sand handy, or extra car mats. Pour the sand, or place the car mats under/around your tires, then get back in and reverse or drive forward, whichever way you need to go to escape the drifts.
Step 6: Just One More Thing...
Should you ever be in a situation to where you are trapped in your car during a winter storm, DO NOT PANIC!! Keep calm and carry on. Keep your wits about you. Don't wander off, you could freeze to death. If you can, call your family or friends. Tell them where you are and that you are ok. Take deep calming yoga style breaths and remember your training. You may need to add things to your kit depending on your area. If you live close to woods, you may need a weapon, but in the city, you probably won't need that shotgun. May the force be with you.
Step 7: *update*
In the dark you will be hard to see. A snow plow could easily miss you and cover you in snow, or a search team could miss you. Whatever the case, signaling flares and/or reflective triangles, blinking lights, basically anything that will draw attention to you.
Thanks to suprspi for suggesting these things:)