Yeah, you should look for a set of the winter 19" wheels. I think many people who live up north have their summer set and when winter rolls in switch to their winter set. Its easier having 2 sets of wheels than to have to have tires removed from the rims twice a year. Plus with 2 sets you can keep your summer sport tires which perform much better than all season tires. If you don't want to buy another set of wheels, a decent alternative would be the Continental ExtremeContact DWS (Dry, Wet, Snow) tires. I have read some good results with them but haven't used them personally. Then you could keep your 20" wheels and not have to change tires when the weather warmed up. I wouldn't imagine they will perform as well as an all season tire, but it should be a huge step up from the sport tires you have now.

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'12 E92 M3 ZCP Stage 2 Tune, Exhaust, Test pipes, GTS DCT Software
'07 E70 4.8i
'07 E92 335i FBO+Meth M3 Suspension Swap and much more 505hp 564 lb/ft tq (Sold)
'89 E30 325i (Retired with 230,000 miles )