Installing on Linux should just require finding the correct package in your distribution's listing. For example, for Debian or Ubuntu, you would execute sudo apt-get install gcc-mingw-w64.

Once installed, the compiler can be used with CGo by setting CC=x86_64-w64-mingw32-gcc (for the C toolchain) and CXX=x86_64-w64-mingw32-g++ (for C++ requirements).