I have the Pirelli Scorpion snow and ice on my "08 GTS and they kick ***!!

 

I'm mounting up some Nokian WR G2s tomorrow - they are one of the only (the only?) "All Season" to get the snowflake emblem. I've previously run the Pirelli's, but this setup didn't go as well in the snow as my S6 with Bridgestone Blizzaks, so I thought I'd try a different tire. And I know this isn't an exact comparo, but all I can say is the Cayenne didn't feel as sure footed as the S6 (and we currently own both cars, so routinely drive them back to back).

I've always downsized the rim an inch from summer to winter and it has served us well, but think (as the other posters mentioned) that this really only benefits in deeper stuff. Seems to me that even on plowed roads, the tire & tread may work better downsized than a stiffer sidewall, but that's just conjecture.

 

I picked up a set of 19x9 GTS replica wheels on Ebay for winters. $530 shipped for all 4. Add in tires and sensors, you're still well below $2k.