Or you could try this ./configure option: --enable-cygwin
I understand it has been built and run successfully under Cygwin.
Alex Peeters put a bunch of work into it. The option is still present in the configure script and I see edits to the Cygwin code as late as 3.0rc2 in the Nagios change log. Should still work by the look of it.
It might be easier to build and set it up on Linux first time though, but giving Cygwin a try might be worthwhile.
I've never used Nagios myself, so am rather confused by the need for windows clients. In my explorations of MRTG I found that SNMP services could be setup with native windows tools on windows boxes, no third party clients needed.
I'll be curious to hear the tale.