Theoretically, your idea is good -- I concur that a tall, narrow tire is best in snow, and like you, I have always used studded tires (I like Nokian Hakkas, and the latest, VII's, are incredible). But now for the bad news:

1) the spare tire's wheel is very narrow, far too narrow for any regular tire of adequate (see below) size to be mounted. Tires of various sizes have an acceptable range of permissible wheel widths (check out Michelinman.com and see their specification charts for any tire to see the wheel widths) -- you will find that the spare tire wheel is too narrow.

2) you need a tire size large enough to adequately support the load (weight) of the car at highway speeds. The load rating is a coded number (e.g., 89, 91, or so for 240's, depending on sedan or wagon) and you will not find a tire narrow enough to fit on the spare tire's wheel that has a large enough load rating to drive safely.