I ride the same bikes I ride all year. My "foul weather" bike, good for rain and slush, is a steel touring bike (Novara Randonee) with cyclocross tires (Avocet Cross K, 700x32c). It has fenders and front and rear racks.
I ride my Airborne Carpe Diem when it's dry.
I confess to skipping days when there's ice, or when it's raining and near freezing, but in the last couple of winters here in Philly that hasn't been much of an impediment.
Growing up, back in Chicago in the 50's and 60's, I rode an old JC Higgins cruiser with balloon tires. I pounded a bunch of roofing nails through the tires from the inside, and then lined the tires with a strip of old inner tube, and these were my studded tires. I could pretty much ride all year around thanks to that bike.
RichC