I bought a used set of 20" genuine alloys with as new Dunlop winters for less than a new set of winter tyres would cost. If you've got the storage this is the best option IMO, easier to swap wheels than tyres and keeps the 21" alloys and PS4s tip top for the summer.
Slightly off topic but could all season tyres be an option? I just put a set of Cross Climates on my old A4 cabby and tried them out yesterday in over 6" of snow, it managed surprisingly well. It is a quattro but being sline has less ground clearance than a racing snake so bellying out (and steaming exhausts) were the main issues, traction was much better than the previous PS4s.