I was forced to do this one time as an educational experience, and while I was able to do it, the amount of hassle that came along with it was unreal. The best advice (assuming you have a windows box) is to program the windows specific code on native Windows. Regardless, you are going to have to use a toolchain that supports the ".exe" file. This is best done natively on Windows, but you might be able to use 'W.I.N.E' or something similar.
If you are using libraries that are cross-platform, and assuming you stick to cross-platform code, it should be as easy as just compiling on the new platform (I use the phrase "should be" lightly).
Do you have any Windows box at all? It can be troublesome to develop for a platform you can't test on.
I missed this the first time, but this is a very real and valid point. It is not good practice to test a game that you want to natively port to Windows in something like "W.I.N.E." You really want a native system to test on.
@EDIT: Added to original answer.