I should preface this by saying that I've worked in the bike industry since I have been an adult working person, and so you generally are harassed for driving your car to work, ha! But, I commuted through 5 winters in Colorado, 5-15 miles each way ( depending on the job) and I really enjoyed it, and learned a lot!
Key things for me:
1. Get a mountain bike for commuting. Now, I own about 3 of these (for racing, riding, etc) but I think a mountain bike makes the most sense for year round commuting if you only want to own 1 bike. Preferably a hardtail of the metal variety (steel, aluminum, titanium), could be rigid, or have front suspension. Sure, wider tires are a bit slower on dry pavement, but riding through slush and ice and snow feels so much safer with knobby trail tires. I never found the need for studs, just ran lower pressure depending on the surface. Mountain bikes usually come with disc brakes (better stopping in all weather), low gears (for your steep hills), and honestly are just more stable for any abrupt moves you might have to make in traffic. Knobby tires also allow you to "bail" aka hit the dirt when you feel like a car is being unsafe. I also feel like I take up more space in the road when I'm on the mountain bike, which makes me feel more visible. You can put racks, fenders, whatever floats your boat on a mountain bike with plenty of room.
2. Bar mitts, Bar mitts, Bar mitts. This cannot be emphasized enough. Just buy them! They are not that expensive, and make a HUGE difference. I went two winters freezing my fingers off in my -5 degree rated ski gloves...nothing takes the chill out of a 2 mile downhill start when it is -10 outside! The bar mitts enable you to wear lighter gloves, which means you have more braking, and shifting function with your fingers. Which means you will be safer.
3. Winter Shoes. This is a big one, and also a more expensive one. I also was stubborn on the uptake with winter shoes, and regret it because some of my toes have never been the same after 2 winters of sub zero commuting in my summer riding shoes. Lake makes in my opinion the best winter shoes out there, but you can't go wrong with 45 North either. If you're on flat pedals, any winter snow boot will function just fine as well, as long as it is WATERPROOF and insulated. I commuted on clipless pedals, so went with a more cycling specific setup in the Lake MX303 shoes...which I purchased new 4 years ago, and they still look perfect.
4. Lights. Not just any lights either, you need bright, day time running lights that are specifically for extreme visibility. I wouldn't ride or commute without a Bontrager Flare R light. My interaction with cars since using this light has been remarkably different. It has an irregular beam pattern which grabs drivers attention, and it is bright enough to be seen a mile away. The front light they make to pair with this light is also excellent, and they both make perfect night time lights for the way home. They are also USB rechargeable, so no pesky batteries to worry about! Don't skimp and buy cheap Blinky lights, it's your life! It's worth it!
5. Fenders. Doesn't matter how cheap they are, most fenders work great. Just get them...nothing worse than a cold, wet butt after a 12 mile ride into work.
6. Cycling clothes. Personally, I never rode to work in the clothing I was wearing all day. You get sweaty, and/or wet from snow/rain, etc...it's just not worth it. Just a pair of basic black cycling shorts works, and in the winter I wear waterproof baggy pants over, and then a basic base layer, fleece mid layer, and waterproof jacket over (if it's snowing/raining). In the summer I'm all about the tank tops( some sort of wicking running top) and riding shorts! The less clothing the better, it gets warm when you're toting your lunch and clothes and shoes!
7. Bag. Make sure it's waterproof, and has enough room for all your crap. If you've got a rack system, awesome! Ortlieb makes great roll top, waterproof panniers. I've found if I'm carrying things on my back, a traditional backpack works best, and messenger bags end up being really uncomfortable after about 2-3 miles. Better to distribute the weight evenly, than killing that one shoulder with all the weight.
I could probably list so many things, but TLDR right? The biggest thing I picked up from commuting so much was always have gear for the worst conditions...I recommended a waterproof bag...not because it rains every day, but why would you have something that would't protect you if it did? We always say here in CO, there's no bad weather, just bad gear. If you're prepared for anything, you'll have way less excuses, and find yourself enjoying the commuting process a ton! I can remember so many mornings being the only bike on the road, because it snowed 6 inches overnight, and it was zero out...it always felt so special, like I had this privilege of first tracks in the snow, with no one else around! Commuting by bike became my mental health time, to process my day after work, or prepare myself for work in the morning. It's the best!
I should also mention that I am a lucky duck now and live less than a mile from work! I feel like I've earned it after 5 winters of living pretty far, haha! It's still cold and snowy, but now I can walk if I feel like it and not worry about all the gear, which is a nice treat.