Windowing applications in the Linux world are based on the X Windows system. If you can remotely login to a Linux system (say, on the CS network) from your Windows machine, you can also start windowing applications on the Linux system (e.g., Emacs, the Greatest Editor Ever!) and have them appear on your Windows screen. You can also use X Windows to get windowing applications from the Windows 10 Subsystem for Linux to appear on your Windows machine.
In order to get them to display on your local Windows machine you will need an X server (the programs that throw up X windows are the clients). I recommend Xming. You can download Xming here. Install Xming using the default values; this will also install the plink PuTTY secure shell (SSH) client. This will give you a way of remotely logging in to remote machines running SSH (e.g., the CS network).
When you first start plink/PuTTY you will see some configuration options.
If you want to run X applications remotely via PuTTY, you will first need to start Xming on your Windows machine. Be warned that X Windows can be slow over wireless because it uses bitmaps rather than vector graphics.
To start a PuTTY session, enter your login information in the "Host Name" text box on the PuTTY start screen. For instance, if your CS userid is doofus and you want to login to goofy.cs.wm.edu, you would enter
doofus@goofy.cs.wm.edu
Then click "Open" at the bottom of the screen. You should then see a command line window and a prompt for your password.