Since Go is a compiled language, this kind of development setup is not as easy as with scripting languages. To compile a Linux binary under Windows, you have to set up a cross compilation environment. The binary packages you can download from golang.org only support the platforms they run on (i.e. the Windows compiler only produces Windows binaries), so you'll have to compile Go from source. This blog post gives a good introduction to cross compiling - make sure to also read the "caveats" section, just in case these apply to your situation. After building Go as described in the article, you will have "clones" of the "go" tool named "go-linux-amd64" ("go-[os]-[architecture]") which you can use to compile binaries for other platforms.
Edit: Dave Cheney has written another blog post on the much improved cross compilation available in Go 1.5 (which is due in August).