Setting the DirectInput/MouseWarpOverride key to "force_edge" fixes use of the mouse ingame. Without it you won't be able to turn around.
The easiest way to set this is to edit the user.reg file in your bottle (in my case it was at ~/.cxgames/Steam/user.reg). Add these lines:
[Software\\Wine\\AppDefaults\\t3.exe\\DirectInput] 1270658822
"MouseWarpOverride"="force_edge"
[Software\\Wine\\AppDefaults\\T3Main.EXE\\DirectInput] 1270658822
"MouseWarpOverride"="force_edge"
You can also do it by starting the registry editor in the bottle, creating the key "HKEY_CURRENT_USER/Software/Wine/AppDefaults/t3.exe/DirectInput" and setting the string value "MouseWarpOverride" to "force_edge", and then do the same for "HKEY_CURRENT_USER/Software/Wine/AppDefaults/T3Main.exe/DirectInput". I am a tad uncertain about if its the t3.exe or T3Main.exe that actually needs it, so I add both for good measure.
