http://bugs.winehq.org/show_bug.cgi?id=15226
--- Comment #19 from Daniel Santos daniel.santos@pobox.com 2009-07-24 17:21:27 --- Thanks! I don't see anything in there that would indicate the cursor/icon patches will help, but if you are in the mood you can give them a shot, I've uploaded them here: http://glest.codemonger.org/files/wine/cursor-work-20090723.tbz2
About 1% into the log file, it calls SetCursor(NULL) to disable it (and again about 60% of the way through). So, as you said, it would appear they draw their own mouse cursor after a certain phase into running the program (before that, they are just using OEM cursors).
I will say that something is definitely wrong because when the program closes, it attempts to destroy each icon twice, I presume this is from CURSORICON_FreeModuleIcons, but I don't know why it would try to delete them twice.