I just noticed that S3 has a registry setting called "GDIMouse". This setting is reflected by the "use colored mouse pointer(if possible)" / "use monochrome mouse pointer" settings. ("Benutze farbigen Mauszeiger(wenn möglich)" and "Benutze monochrimen Mauszeiger" in my German version). Changing this Setting has no effect on S3 in Wine. I suppose S3 fails to draw its own mouse pointer in Wine and falls back to the GDI one.
In that case, you need to do a +dinput,+cursor,+ddraw,+event trace to see if it puts DInput in 'EXCLUSIVE' mode and also if there are no cursor calls once the game starts (as there is no need to change the GDI cursor if the game is using its own).
Lionel