Cygwin is a Unix-like environment and command-line interface for Microsoft Windows. Its core is the cygwin1.dll library which provides POSIX functionality on top of the Win32 API. It can be used as a build environment which targets Windows directly and for which output doesn't depend on cygwin1.dll.
Installation is done through cygwin's package manager: setup.exe.
As part of the numerous packages in cygwin, there are cross-compilation toolchains which target both 32 bits and 64 bits; their names start with “mingw64-”.
Once they are installed, they should be used according to the general cross-compilation approach.