Completely doable, though you'll have to breathe slower because of the cold air while putting down same or more power. Go train your lungs starting now, you'll need it.
Salt and ice murder drivetrains, and snow washes off both wet and dry lube after one ride. You don't necessarily need a complete beater bike, but a sacrificial drivetrain and a set of fenders would go a long way.
Dress for 10 degrees less than you would on foot, winter pants AND underpants are a must if you don't want your balls to freeze over.
Take the sidewalk to avoid slush and potentially crashing cars, don't be a hero.
Pay attention to the road surface, studs are very slippery on concrete and tile. Having mismatched tires with studs on front wheel and none on the rear is a decent solution to that issue, it'll roll better too.