Get a set of 4 steel rims and put Michelin X-Ice tires on them (or another good make).
This will prevent salt damage to your alloy rims and the X-Ice tires are amazing on my GXP.
I was worried that my V-8 would be unmanageable in the ice and snow, but the X-Ice tires help the Grand Prix to handle as well as my 4x4 Pathfinder ever did.
Hope this helps!
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2006 Grand Prix GXP, Black Cherry