I agree, check the website for Tire Rack, Discount Tire, or even a local tire store chain. They will list your original wheel and tire sizes, plus offer you "plus-size" and "minus-size" combinations that will fit your car. And a taller tire on a smaller wheel (same outside diameter) will give you more sidewall, more cushion to soak up those nasty winter potholes. Narrower tread can also help traction in the snow.
I did this for my G8 (not a GXP) and went down from the factory 18s to 17s. Although you may find it very difficult to find steel wheels that fit in sizes above 16. But the money I saved on tires (over buying the larger 18 dia winter tires) paid for the set of new aluminum wheels to fit them.
I ordered a set of Bridgestone Blizzaks on new wheels (17s) from Tire Rack, and they were delivered in two days, right to my driveway, all mounted and balanced. If you can't mount them on the car yourself, you can even have them delivered to your local service center.