All-season tires are a compromise all seasons. Rubber gets harder as it gets older and as it gets colder. If you're running summer tires, don't even think about using them when the weather gets colder, regardless of whether there is ice or snow around...they'll function not much better than slicks in the rain.
Worse comes to worse, the 'stock' wheels on the BMW GT are 18", so there should be at least a few available in that size that fit.
Unfortuneately, there aren't all that many run-flat snow tires that fit the GT, especially if you want to maintain at least a V-rated tire.
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