CnC 3: Tiberium Wars uses animated cursors right from the outset.
A few google searches reveal that these don't seem to be supported in the current stock version of Wine or cxgames.
Consequently, though the game installs well and runs well, I can't see the cursor, and so can't really play.
Hopefully proper support for animated cursors will be integrated into cxgames soon, and it'll be playable, but until then, we'll just have to wait.
edit:
The 'Tips & Tricks' say that you get your system cursor, but I think that was an older version of cxgames, now you just get nothing.