First you need to install cygwin/x with openssh packages as well as X11 Windows System:
You also need to set DISPLAY environment variable before the following steps:
$ export DISPLAY=:0.0
Next, open cygwin terminal, before use ssh to remote connect, run xwin:
$ xwin -multiwindow &
You can test it with
$ xterm &
to see if it works.
After running xwin stand alone, you can use ssh to connect to linux machine:
ssh -Y [remote-host]
$ firefox &
to see if Firefox at the Linux machine can show up in your server host.