Getting Cygwin X Working Nicely in Windows
I’ve had Cygwin X working OK for over a year now and really enjoy being able to run remote X applications. What I’d like even more is to run them without a second thought. If you double click cygwin.exe after installing Cygwin X you’ll be reminded of its constant presense because of the minimized dos window that lingers as long as you run the X server.

The solution? Change your shortcut to XWin.exe from something like this:

C:\cygwin\usr\X11R6\bin\XWin.exe -multiwindow -clipboard

to something like this:

C:\cygwin\usr\X11R6\bin\run.exe C:\cygwin\usr\X11R6\bin\XWin.exe -multiwindow -clipboard

I additionally changed the icon from the R to the traditional X icon. Now your only reminder will be a small X icon in your notification area. This is configurable so that if you prefer, there won’t eben be a an icon in the notification area.
In case others are trying to figure out how to do this, here are some search words that didn’t work for me: Cygwin X hide dos console window