Get some studded tires. It's worth it. Fat knobbies are useless in icy conditions. Don't worry about the width.
For riding in the city a 1.9 studded tire is all you'll ever need, fat mountain bike tires around 2.3-2.5 is an overkill for riding on the roads and they are no better on snowy roads/mups then a 1.9 winter tire.