I've driven mine for two and a half winters in Boston. I have a set of winter michelin tires on dedicated winter wheels, 8 inches wide. I don't have spacers on it, but I should, the rear wheels are really sunk in.
Learned to drive in Anchorage, AK in an '85 4WD Nissan pickup truck. Switched to a Mazda 2WD B3000 in 2003. Finally got my Z in 2011 and haven't looked back.
I've never driven a modern sedan in the winter, but coming from a pickup truck, I can say without hesitation that a 370z with winter tires is a fine car as a daily winter driver. A good set of tires provide plenty of traction to start moving from a dead stop on snow, plenty of traction to make it up a snow covered hill if you're already moving. The electronic traction control and ABS brakes will pretty much prevent you from ever spinning out or sliding (unless you tell it to, that's easy enough). If you live in a modern, *northern* city, you never have to worry about snow clearance. The plows are out long before it gets deep on the roads themselves. I have private (unheated) garage parking, I can't say what it's like to have to dig out a Z from three feet of snow. I wouldn't want to do it.
I wash my car at least once a week, or more often as conditions and salt require. I always get the undercarriage wash. I get a detail and wax a couple of weeks before winter hits, and a detail and wax a couple of weeks after spring has started.