Cars (in general) don't handle well in the winter because of the tires. Is the 370z and ideal platform for snow... NO. If you can keep the beater i would do that.
However....
A friend has a Z4. On days when it snowed even a half inch, he couldn't get his car back into the garage. I grabbed his credit card and ordered Blizzak WS60s with Steelies for him. $800 later, It now goes better in the snow than his wife's Accord on all-seasons.
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