A number of years back I was driving from Vegas to Denver to visit my sister. It was April and I figured the risk of bad weather was minimal. I got caught in a snow storm about 50 miles outside of Denver. I slowed down and was doing 15 in a 65mph (as was other traffic). I could feel the rear end dancing a bit but I figured at that low speed on a 4 lane mountain interstate I'd be OK if I lost it. Well the rear end came around on my and I ended up backwards on the inner shoulder. I waited for traffic to pass and got her turned around. I continued to limp for a few more miles trying to find an exit with a place to stay for the night. At that point once it got dark I simply limped the car along the shoulder with hazards. Then going up a hill the car just slowed to a stop. I was stuck. About 30 minutes later I was able to get some traction and get off at the next exit for the night. The next morning when I got into Denver I got new tires, the old ones were worn out.
That being said, even with new tires the Z is kinda squirly and lacks any type of stability control. If you live in an area that sees prolonged periods of snow, get a beater. I suggest a 1990 Subaru Loyale with 4WD. Pushbutton 4WD on the shifter, good on gas, and cheap to buy and maintain.
"The 300ZX Turbo is a dance; it's a song; it's rolling, roaring automotive art. There is no color that doesn't suit it. There is no mood-lifting chemical substance it can't replace." - Automobile Magazine