I had a '99 Z-28. Never got stuck once. I used the all season 16" wheels in the winter, and the 17" SS wheels in the summer. I put 2-3 bags of salt in the back, and had traction control. I had a major hill to climb as well, and still never had an issue. Drive like there is snow on the ground and you should be fine. I plan on driving in the winter. I'm along interstate 74 in Illinois.
I can't imagine having trouble if you get the winter tires.
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