Quoted By:
I think with warm clothing and patience you'll be able to cycle through anything. The issue is really time. You have to get dressed with your layers, cycle slowly through snowy shit, then undress at location. Doable just a consideration, shit will take awhile.
This is a serious undertaking you're putting upon yourself, just be conscious it will be hard.
For your bike, I'd recommend some fat tired 26inch rigid mtb, doesn't need to be good. Put fenders and studded tires on it. Get a rack and put a milk crate on it.
For clothes, I'd recommend checking out 32degree for cheap synthetic undergarments. You will want some leggings and undershirt. A neck gaiter. Hat. Goggles for when it's really snowing. Gloves (consider those over-handlebar mitts). And some baggy beater pants and jacket for cycling in. Some rubber boots probably would help. Carry extra clothes to change into at work, trust me it's necessary.
I'm in upstate NY, we get nasty winters my citys average snowfall is almost triple anywhere else. Asides from the above tops about staying warm, you also need a bike you dgaf about. Because it's gonna get fucked the Fuck up.