You live in a place with lots of cold and ice. I recommend getting studded tires and putting them on a winter bike. They are fantastic. Nokian (NOT the phone company--common mistake) makes the best studded tires with carbide studs, but there are less expensive brands, too.

Not to add to your worries, but it's also best to stay away from puddles because you don't know how deep they are. The water could disguise a deep rut or pothole.