I don't drive my 370z in winter, but I used to drive my 350z all year around.
You need a set of good snow tires, not Hankook, at least Bridgestone or TOYO.
Like steve1ddd said, traction is not really a problem, but clearance is, 2 - 3 inches is not a problem, but more than 5... you gotta be careful.
The VDC is excellent, not only twice I mention in this forum I was benefited from it helping me get out of a crash.
Overall, if you are thinking about driving the Z on snow, I'll say as long as you put on a set of good snow tires, you'll be fine.
A side note to you, if you are going to drive the Z on snow, make sure you will have an under-car wash for it often enough to make sure no salt or dirt stick on the car.
