Hey man, I was going through the same issue that you are going through right now. A little about myself, I live in West Virgina, and work in the Washington DC area as a professional firefighter. Unlike other government employees, we get no liberal leave days, and when everything is closed, we still got to go to work. I was thinking I would just take it easy with my Z, as it was my daily driver, and I could get through the snow.... THEN REALITY SET IN!!
The Z is a sports car, and it was built as such. As the temps went below the 40 degree mark, the tires started losing their grip, and what little amount of ice I did drive over was terrifiying. Sure, you could put snow tires on your Z, but that doesn't change the fact that it still has 330 horses going to the back wheels, and the car sits close to the ground. So, even if you could get over the fact that your have a lot of power to the rear wheels (which are, by the way, summer performance tires), you wont be able to get far, as it is close to the ground.
Some members on this site have outfitted their Z's with winter tires and rims. I believe that is going to run you somewhere around 1500 dollars. That is great, but remember, you are still going to be subjecting your car to the salt, and overall grime that is going to get all up over and in your car. Not to mention the overall danger of wrecking it! Do yourself a favor, and get a beater.... I just purchased a 96 Jeep Grand Cherokee, fully loaded for $2000.00 . That is 500 more that what a set of winter tires and rims will cost you, and you can keep your Z in the garage. I know for a fact that Jeeps don't hold their value AT ALL, and you can get a nice one for just a little more than you could by the tires for.
The Z wasnt made for the snow, and you will only be subjecting yourself to a very long, stressful, and perhaps costly winter!
Hope this helps!
On another note, there are members who drive their Z's during winter, through snowy conditions. My hat is off to them, they are better drivers and got more balls than I do!