Ref: http://x.cygwin.com/docs/ug/setup-cygwin-x-installing.html

Download the installer (setup.exe) from the official site, and follow the following steps:

• Choose Install from Internet.
• Specify Root directory (I chose C:\cygwin) and Install For (I chose All Users).
• Local Package Directory.
• Choose Direct Connection.
• Available Download Sites: I chose http://lug.mtu.edu.
• Choose the packages you need. I only installed the following two packages, which still worked:
  • xorg-server (required, the Cygwin/X X Server)
  • xinit (required, scripts for starting the X server: xinit, startx, startwin (and a shortcut on the Start Menu to run it), startxdmcp.bat )
• Postinstall script error: You might see error message as follows after the installation. It does not matter here.

Package: Unknown package

    autorebase.bat exit code 1

• Create icons: Up to you.

• Setup your session. It is easy in putty. You can enable the option Enable X11 forwarding from the left panel Connection->SSH->X11.
• Enable XWin server on Windows. You should be able to find the shortcut XWin Server in your start menu.

Nevertheless, when i connected from my apartment to a machine in Ohio via 15MBps internet bandwidth, the connection was slow. So far the speed is affordable inside Amazon with ethernet connection though.