The down-side to the STI in winter driving is the fact that you can't seem to minus-size the tires (narrower tires, smaller diameter rim) very well, because of the size of the front brake calipers (I suspect the EVO might have the same problem).
This is a minor downside though, even with wider tires and a larger diameter rim than you'd normally want to drive in the winter, the STI still behaves very well (provided you have the right tires).
I'm really kind of surprised Jeremy didn't mention tires, considering that's THE most important part.
The stock tires on the STI for example, are awful in the snow. The manual mentions four, five times that you cannot drive them in the snow, and believe me, they are horrible even in a little bit of a hint of snow.
Personally I bought a set of dedicated winter rims (Compomotive TH3) and tires (Nokian WR) that seem to work very well.