I had an old copy of UT2003 left over from my pre-Mac days when I was still using a PC. Rather than throw it away, I thought I'd fire it up on Crossover Games 8.0 and see how it runs.
When I first tried to play it, I could see the weapon and the HUD items, but I could only see vague-gray shapes in a yellow fog as far as anything else went. After messing around with the settings for awhile, I figured out a solution.
From the Crossover menu, go to 'configure' and then 'manage bottles'. Alternatively, you can click the 'manage bottles' link next to the little wine bottle on the Crossover Games screen.
Choose the bottle where you installed UT2003, and go to the control panel. Select 'winecfg' and click 'launch selected item'. Go to the graphics tab and UNCHECK the box that says 'allow pixel shader (if supported by hardware)'. The yellow haze should now be gone, and you should be able to see what you're doing.
However, more bad news. Mouse controls are messed up on UT2003. The mouse is out of sync with the game window, even in full-screen. Unfortunately, I have no solution to this beyond this simple band-aid: in the game, reconfigure your controls so that you don't have to use the mouse. It gives you a little less flexibility in where you can look (compared with a native installation), but it's better than having no control at all, and the game is at least playable.