I'd put decently fast 28s on the commuter if roads permit. Save the good bike for longer days and better weather. (If the commuter is not a drop bar bike I take that back. 20 miles is a long ways to go if you cannot get comfortably aero in a headwind.) Ride at least two days a week because with just one, it will feel hard. Two becomes routine. And (say) Tuesday, Thursday, weekend - you'll be rolling when spring hits!
Actually I might start on 32s or 35s just to get to know the road and its hazards before I moved up to 28s in the dark. And - important - first ride is on a Sunday! Maybe with a map so if any of it is sketchy, you can try other roads.