If I decide to ride in seriously crappy conditions, I'll put some rain tyres on. They're still 23, so clearance is ok, and made from a softer compound with a relatively deep profile, so traction should be decent on cold, wet pavement. Snow and ice would still be a problem, but snow doesn't remain on the roads for long in a city, and where it's icy, only studded tyres would help anyway.
Funny thing is, knobbies would fit fine on my (road conversion) bike, but for my recently installed fenders... which I will need in the winter. The maximum that fits under them is like 25mm