While I can't answer that question with a definite I'm reasonably certain: yes.
Firstly Obj-C support is built into GCC which as a cross platform compiler should run on Windows.
GNUStep is an open source effort to clone the old OpenStep frameworks which became Mac OS X when Apple bought NeXT. See http://www.gnustep.org/
You might need to use cygwin (http://www.cygwin.com/) which is a set of a dll and other tools to allow you to compile and run otherwise UNIX only programs.
I know this is the Mac OS X section but it's a worthy question, and so I for one would be interested to know how you get on.