I kept the standard 17" polished rims for winter when I upgraded my summer wheels. YOu cannot go 16", nor do I think you would want that in the GT if you are going to drive it in the winter.
My 99 GT was a great winter car as it was the first year with the traction control. I had Goodyear M+S tires and were quite good, if a little noisy.
This time I went with the Michelin X-Ice tires, based on my experience with the Michelin Arctic Alpin, which i have had on two cars. On my previous ride, a Volvo S60 T5, the car was sensational in the snow, especially with DSTC.
Now the Mustangs only have traction control, but the benefit of RWD coupled with TC will make the car a good winter car.