TLDR; no, libuv doesn't work in Cygwin just yet, see at the bottom.
I tested using the master branch (9d3449852bd35c9283948186d0259c1bf73b8579 or later)
I installed the following in the cygwin setup
- gcc-c++ make cmake pkg-config libtool
Check the pull request for the changes and the main issue for discussion. If you run into trouble check the Known Errors
section at the end, or drop me a comment.
Before you start you need a Mingw-w64 toolchain for Linux, try installing the mingw-w64 package (Ubuntu, Suse, Fedora?) or get it from the Mingw-w64 website.
$ mkdir deps-mingw
$ cd deps-mingw
$ cmake -DCMAKE_TOOLCHAIN_FILE=../cmake/mingw32-w64-cross-travis.toolchain.cmake ../third-party/
$ make
$ cd ..