This was the solution I chose (although I ticked the answer that directly answered my question):
As Clive commented Drush needs to invoked in the Drupal environment itself. Seems obvious now, but it didn't occur to me initially. Instead of carrying on developing in my server space I decided to start developing my sites on my local machine. I downloaded and installed the Acquia Dev Desktop on my Windows PC. To get the Drush command line you can use the Drush Windows Installer. Now you're ready to go.
Start the Drush command line. Choose the directory where you want to install Zen, for example:
C:\ProgramData\Drush> cd c:\users\sites\mysite\sites\all\themes
I had to create the 'themes' folder (the Acquia install didn't create it for me). These are the commands I used to install Zen, create a sub-theme and enable the sub-theme (see kiamlaluno's answer for more info):
C:\Users\Sites\mysite\sites\all\themes> drush dl zen
C:\Users\Sites\mysite\sites\all\themes> drush cc all
C:\Users\Sites\mysite\sites\all\themes> drush zen "mysubtheme" --without-rtl
C:\Users\Sites\mysite\sites\all\themes> drush en mysubtheme
There is no command for setting the theme as default as far as I know, but everything else seems to be done. Much quicker than doing it manually!