We are going to adapt the 10 essentials of hiking & camping for winter road travel: These should always be in your car to make emergencies easier.
1. Extra Food: Store enough food for the normal number of people you take in the car so they can be fed for one extra day. A good option to this is to toss in unused freeze-dried meals, instant oatmeal packets, or energy bars from a previous camping trip. You can use The Wild Dirt Camp Mug as a bowl to eat your oatmeal or camp meals. It's great to have extra food in the car for when you are hangry too.
2. Extra Water: Keep a jug of water and even a water filtration device like a LifeStraw or purification tablet in the car. Replenish the water so it doesn't get stale. Keeping the water in a larger gallon jug instance instead of multiple smaller water bottles can help keep the water from freezing but you might want to leave headspace in the container to allow for expansion if the water does freeze.
3. Shelter: This is an important Ten Essentials item and your car can act as that shelter but you could also bring a tarp too, encase you need to sleep outside the car.
4. Navigation: Keep a paper road map in your car and if you are going someplace like a National Park bring a paper map so you can find where you are if you lose signal. If you know how to use it bring a compass. If you don't know how to use a compass, learn. GPS and personal locators are also good if you have the money but a paper map is always more reliable.
5. Flashlight: Let there be light! A flashlight is a great item to have in the car encase you need to change the tire in the dark, walk down an empty road to the nearest gas station, or try and flag someone down. Get a headlamp and it will make your life easier. Especially when you need both hands to change that tire.
6. Knife: Doesn't have to be a giant Crocodile Dundie knife. A multitool is even better because the wrench and other tools can come in handy to repair something.
7. Fire Source: Matches are a good basic essential item. Get some that are waterproof and can strike on anything. Keep it separate but bring tinder to start a fire or an extra camp stove and/or lighter if you have the money. You can also use these along with a metal cup or pot to boil water for your extra water requirement.
8. Sun Protection: Easy one since you probably already have a set of sunglasses in the car but dont forget sunscreen or a hat to keep the sun off of you. Even in the winter, the sun can be intense.
9. Frist Aid: bring a little kit with you to stop bleeding, bandage yourself up, medication could be another item to add to that to make your trip more enjoyable.
10. Extra Clothes: Like food make sure you bring enough extra clothes for the average number of riders in the vehicle. In the winter you might want to include heavier boots, gloves, an extra jacket, or fleece blanket to keep you warm.
Beyond these adapted 10 essentials I wanted to mention some specific winter car additions. such as windshield wiper fluid, Ice scraper/snowbrush, a small shovel, something to help you with traction such as cat litter which also helps with weighing down your tires, or a tread board that you can stick under your wheel and help you get more traction on ice and snow.
Remember, regardless if its winter there are your normal vehicle emergency kit items you should keep with you such as jumper cables and/or battery powered car starter, pressure gauge, spare tire and tools, fix a flat, owners manual, Duct Tape, WD-40, road side assistance tools like flares and reflective triangle.