I would probably say a full suspension titanium 29er mountain bike with 1.5"-2.4" studded tires, with backup wheels w/ non studded tires stored in the house for when studded isn't needed. Frozen over plowed roads can get bumpy, and a large rock or frozen raccoon may be hidden under a spot of snow, hence the full suspension.

Front and rear racks would be wanted, although limited for this bike. Perhaps a frame bag to keep center of gravity inside of bike. Small backpack. Handlebar bag on straight bars for head and hand wear. Large seat pack to store wind proof and warmer clothing. All the survival essentials to fix the bike on the road and even to make a fire.

Maybe some aero bars to fight a windy day. Hmm, lots more

Ritchey adjustable stem would be wanted...

Or, a tadpole trike, depending on path.