A snow tire works best when it is (1) as narrow as possible and (2) the aspect ratio (the middle number on the tire) is as high as possible. In plain English, you want a narrow tire with a tall sidewall, because this combination allows the tire to "bite" in the snow when cornering.
This is a long way of saying: you might look into getting the smallest diameter rims that will clear your brake setup for winter use. You will have lots of options in 16" and 17" tires.
For tires: a good value is the General Arctic Altimax. I have these on my wife's Subaru WRX in 17" size. These are virtual copies of the Gislaved Nordfrost 3, an excellent snow tire.
I have an '06 GT 'vert with the 18" Fanblade rims. In the winter, I have a set of 4 Dunlop Winter Sport tires . I am very impressed with these. I drive my car year round.
I use Michelin X-Ice Xi2 in a 235/55/17 OEM size on my OEM "bullitt" wheels. I think they made them in a 225 size, but I didn't want the car to feel too squirmy on dry roads.
I agree with the fellow who said you want the skinniest, tallest tire you can get. Most of the time a good rule of thumb is to get the OEM wheel setup from the base model of your car. The Mustang does have a V6 model with 16" wheels, but a 16" wheel won't clear a GT brake. So you're stuck with 17s as your "smallest" wheel option.
You must have 4 snow tires for the concept to work correctly. 100% different driving experience. Your car actually drives in the snow.