It is possible for you to run graphical programs remotely from your windows box. That is the beauty of the X-Window system. It will require a lot of preparation of both computers to do, though.
For the windows box: you will need to install an X-Windows server. There are many available out there, but the free-est one I found is
Cygwin/X. To use SSH tunnelling, you will also need an SSH client (PuTTY will work well).
On the Linux box, most of the software you need is already there, You just need to configure it. There is a lot of documentation out there on how to set up SSH and XWindows:
http://www.cyberknights.com.au/doc/P...ing-HOWTO.html and
http://www.tldp.org/HOWTO/XDMCP-HOWTO/ssh.html may be a couple of good places to start looking. As well, you can search for documentation on the subject in google.
Good luck getting everything set up.