Yes, you will need an X server for Windows. These are the open-source implementations I know:
*
Cygwin (which provides a Linux environment for Windows, with command line and standard Linux tools) includes
an X server.
* Alternatively, there is
Xming which provides an X server without the whole Linux environment.
To forward X in the initial Putty screen you go to Connection -> SSH -> X11 -> Enable X11 forwarding. The X server needs to be also running for X applications to display.