Yes, you can run graphical programs such as NEdit over SSH. To do this, you'll need an X server installed on Windows. Cygwin/X
are two such (free!) ports of X to Windows. There's an option in PuTTY to allow X11 forwarding and you may also need to enable it on the server as well (i.e. in your sshd_config, which should be in /etc somewhere. It resides in /etc/ssh on my system (Slackware)).