Experience is a wonderful teacher here so...
Start riding now/keep riding
Don't stop riding - be an every weather all conditions rider
Commute if you can or have a purposeful routine for regular riding - you might modify your route a bit for winter riding safety
Have fun riding - enjoying riding just to ride is an important part - slow down a bit, be safe, it isn't a race ( unless you find a local winter racing community )
check for a bike co-op or volunteer run bike shop or something like that in your area - they are good contacts for all weather riding, bike maintenance and repair, your local conditions, some even run classes or courses on winter riding - good folks to know.
You don't need a 'special' bike, but tires can make a difference, but everyone says 'so you have a fatbike?' when they find out I ride everyday all winter - no, my mountain bike is fine, but I have ridden 27x1.25 too on the pack or sidewalks - here (the cold part of Canada) sidewalks in the suburbs are free game in the winter for siding safely.
you don't need a single set of special clothing, but you need to adjust to the weather, layering and unlayering for 5 to 10°c increments, but as you are riding regularly and the weather gradually changes you figure it out. I wear my cleats with wool socks and sometimes my boots if it is really cold. I have thin gloves, thicker gloves, mittens and glove shells to mix and match. Think 'cross country skiing' gear to control for heat and moisture. You will definately dress lighter than you do for walking in the winter. You probably already have everything you need, start with that.
You can get Frostbike by Tom Babin from your local library. He has some videos and articles around too.
https://www.amazon.ca/Frostbike-Pain-Numbness-Winter-Cycling/dp/1771600489
This book is an excellent read.
I ride my old 90's mountain bike. I have ridden it with regular tires and studded tires. You can do either. You can get a studded tire for <80$ at MEC. If you can afford 2 that is awesome, some just like one on the front for steering control on ice, some may disagree. I have ridden an old single speed coaster brake junker with rotting 27x1.25" tires and it works fine too. Coast over slick ice, standing, butt off the seat, with one foot on the pedals and the other dangling = low centre of gravity.
Start commuting now and don't stop. It helps to ride your way through the seasonal change. It helps to make riding the default option and not be only a fair weather rider. It is ok to get wet once in a while. Leave an emergency change of clothes at work/school if you can. Adjust as the weather changes.
Check your community for a community bike shop or bike coop - a place with tools where you can fix your own bike - they are great places for advice, sometimes have that bike you need for winter riding if you are looking for a second bike.
Feel free to ride the sidewalk through that underpass if there is one, or extend your route around it - on heavy snow days the sidewalks are often cleared before the streets - use your disgression - if there are no pedestrians, I will ride it.
Dress for cross-country skiing. Wear a snowboard or ski helmet. I start at -5 to -10°C. Use a cut off t-shirt sleeve or buff/tube/belackava under your regular bike helmet for the transition weather. For a 15 min ride you might even get away with wearing your work clothes and a thin layer over top if you don't ride for a sweat.
Leave your bike in the cold if you can. Melt and thaw and moisture can be a killer.
Put a shower cap over your helmet for rain.
Street lights help you see, bike lights help you be seen. ~$15 white blinky on the front and ~$15 red bliky on the back is sufficient.
The first snow or the heavy snow is nice. The hard stuff is the re-frozen melt and thaw chunks and ruts of February. It is not insurpassable, it is just technical riding - you will arrive at your destination with your mind buzzing ready for anything, with a smile, and sometimes a story.
Some rear racks are a good enough rear fender. Zip tie a plastic or cut up milk jug or other improv extension if needed.
There isn't one right way. Be flexible. Be adaptable. Have fun. Be humble. Take it easy. Embrace adversity. Your second season is always easier than the first ;-)
Also: (MEC Winter riding advice)[https://www.mec.ca/en/explore/get-ready-for-winter-riding]
You can get Frostbike by Tom Babin from your local library. He has some videos and articles around too.
Consider reading Frostbike by Tom Babin. It was quite an entertaining read from the Calgary based author.
I totally agree with what the other commenters have said. Studded tires are awesome.
http://www.amazon.ca/Frostbike-Pain-Numbness-Winter-Cycling/dp/1771600489