I work as a sysadmin at a company making a slow switchover to Linux, and I've experimented with this a bit. You can greatly, greatly limit the damage any virus can cause through wine by unmapping it's Z drive from the wine configuration menu.
By default, wine maps / to Z. I can see why they did this, (wine can only run applications within a mapped drive) but it likely needs to be undone across the board. The best alternative would be to create a unhidden wine folder in the user's home directory and map that in wine.
If Z is left mapped to /, then a windows virus can run rampant all throughout your system.