You can use the mingw32 cross-compiler under linux.
Have a look at this wiki-article:
http://wiki.codeblocks.org/index.php?title=Cross_Compiling_wxWidgets_Applications_on_Linux.
I have written it for cross-compiling with wxWidgets, but the setup for the compiler should be (nearly) the same, even if you don't want to use wxWidgets.
You have to set the appropriate build options for windows of course. That means you cannot use a project created by teh wizard for the linux-version of C::B.
There is no cross-compilng project (at the moment).
Problems of C::B for windows running under wine are most likely issues due to the incomplete windows api of wine and can therefore not be fixed in codeblocks.
Wine is an emulator and it is not yet complete.
But I use it to test cross-compilations under linux and that works (more or less good).