Easily run a Linux app remotely under Windows with Cygwin

Make sure xorg is install on the Linux system.

In Cygwin install:
xorg-server xinit font-adobe-dpi-100

In a Cygwin shell run:
startxwin
export DISPLAY=:0.0
ssh -XC remotehost

Then in the ssh shell you can launch commands, e.g.:
xcalc &

References & info:
Cygwin/X User’s Guide; Chapter 4. Using Cygwin/X; Displaying remote clients

Cygwin/X User’s Guide; Chapter 2. Setting Up Cygwin/X

Ubuntu/Linux Blog | Up Ubuntu; How To Configure The X Server To Accept All Users – Ubuntu

Server Fault: start dummy X server for user logged remotely