I've driven both the ASX and the ZE-512. I would never drive either in the snow if I could help it. I also really prefer the Falkens. They grip better in the dry and evacuate water better as well. Treadwear seems to be similar.

-Philip Maynard '95 Contour [71 STS | Track Whore] '97 Miata [71 ES | Boulevard Pimp] 2006 autocross results