I live in the Cleveland area and have been commuting for the past year, including winter.
I look at it as a winter sport. People ski, ice skate, go sledding/coasting, or just enjoy a walk on a snowy day in December. I ride my bike.
I love the experience of being the first set of tracks on my street quietly crunching through a fresh powder. Once I hit the main artery at the end of my street the roads along my route are usually clear enough to allow for easy pedalling.
Watch the weather to dress accordingly. Waterproof items such as a rain shell (wear layers), boots and gloves can save the day. Give plenty of time for riding and resting as the rest time also allows clothing to dry. When I commute I can hang my gear in a locker at work and things usually dry out over an eight hour shift. Riding cross country might not allow that.
There are lots of sources online that cover equipment. Make sure you have a good set of fenders. The front fender benefits from a flap that almost touches the road. This helps protect the bike and rider from any salty, slushy spray. I rode an old 21-speed mountain bike last winter on 26" x 1.25" tires with an inverted tread and no knobbies and did just fine. I went down once on a sloped patch of black ice.
There are plenty of ways to enjoy Winter. Folks who live in northern states and complain about snow are living in the wrong place. If you think riding in snow sucks, then it will. Read up and prepare yourself with good gear and a little knowledge from those who have gone before you and you will experience something wonderful that you can share with folks who ask.
And be sure to slide sideways. A good, old-timey classic fishtail from your youth, only without the loss of tread.