Most of the best tips for driving, maintenance, etc, are being argu—well, discussed—in these comments. I don’t really have anything to add to what is being said. What I will give my spare change on is what you carry in your vehicle to help you in the extreme likelyhood that you will encounter a situation that requires you to either stay in your potentially non-running vehicle until help arrives, or to exit the vehicle and go to where help can be found. How much you need to pack depends largely on what your commute is like - you probably won’t need mountaineering gear to get home if you pass three gas stations and a Waffle House on the way.

Between November and April, I always have the following in my vehicles:
1. AAA Card. Believe it not, AAA is still a thing you should have, and it’s worth the cost after just one tow out of the ditch.
2. A way to charge a phone that is not the vehicle. Get one of those battery bricks and keep it charged. Many cars don’t have working 12V power if they aren’t running.
3. A good Flashlight that works when it’s cold, because some don’t.
4. Winter clothes. I bought cheap (but name-brand), waterproof ski jacket and pants off ebay that pack small and stay in my car. Hat and gloves, at least two pairs of socks (wool or synthetic blend). NOTHING cotton. Jeans are a no-no, and even a nice warm Carhartt coat won’t protect you very long against freezing rain. Boots too - get some cheap snow boots, or something you can wear over your shoes. Even those rubber boots that will fit over 2-3 pairs of thick socks are better than your athletic shoes. Wool or poly fleece long underwear too.
5. Hand warmers
6. A gallon (or two) of water. Remove about a pint, squeeze the jug until the water reaches the top, then reseal. This will allow the water to expand when it freezes. Add a bottle or two of water using this same method - you can thaw it by sticking it inside your coat (as long as you’re still warm). Use screw caps, nothing that has a pop-off lid like a milk jug.
7. High-calorie granola bars of some kind. Cliff are good, or the brand of your choice. Nothing “low-fat”, those 90-calorie bars aren’t going to help you much.
8. Tow rope, rated for your car
9. High-quality snow brush and scraper. Carry two.
10. Small shovel
11. Small tool kit with jumper cables, wrenches, pliers, fuses, testers, etc.
12. Jug of windshield washer fluid that de-ices
13. A “survival tarp”, one that’s reflective on one side. Those “space blankets” are nice but tear so easily they’re almost not usable.
14. Sunglasses. If the sun comes out, snow and ice get really bright.
15. Road flares or signal of some kind if you break down at night.

I’m probably forgetting some stuff - I tend to keep a lot more than that. I usually throw in a bivvy bag, small iso-butane stove and pot, snow cleats, etc.

One aside - notice that my list does not contain kitty litter, which is something I’ve seen on every “winter driving” list ever. I have yet to encounter a situation where kitty litter would have helped my car get enough traction to extricate myself. So I don’t carry it. If litter has worked for you, please explain the situation to me.