In the past it was necessary that you build your project from the platform you intend to target, each platform. This may be a bit a pain in the but for indie devs who don't have 3 different computers or dual boot. So fundies has decided to start our cross compiler abilities and has created a nice patch for everyone.
Here is me testing it on Ubuntu...

**** Prerequisite Packages *****
sudo apt-get install mingw-w64-i686-dev g++-mingw-w64-i686
***** Instructions *****
1) Install ENIGMA
2) [snip]cd your_enigma_install_directory[/snip]
3) [snip]wget
http://awesome-toons.org/WinPatch.zip[/snip]
4) [snip]unzip
WinPatch.zip[/snip]
5) You may optionally install WINE Emulator to ensure your game built correctly before testing it on Windows if you are on Linux
6) Go to ENIGMA->ENIGMA Settings and set audio system to SFML or None as OpenAL does not work with MinGW32
7) Set compiler to MinGW32
8) Test compile an empty game
9) You should be good to go!

***** Running Games *****
32-bit Debian or Ubuntu : [snip]apt-get install fglrx-glx or libgl1-mesa-glx or nvidia-glx or nvidia-glx-legacy-96xx[/snip]
64-bit Debian or Ubuntu : [snip]apt-get install fglrx-glx-ia32 or ia32-libs or nvidia-glx-ia32 or nvidia-glx-legacy-96xx-ia32[/snip]
Please give feedback and suggestions and discuss the future development of this in this topic.