I really like No Machine (either FreeNX or www.nomachine.com
Install the server on Mint and the client on Windows.
The connection, however, is based on your networking where your computers live.
In my case, I have Linux at work and Linux and Windows at home. To get to my Linux at Work (or at Home),
I have to vpn into my company's network so my ip address is visible on the same network. After I'm in, then I can use the No Machine client
(there are gnu versions, but I use No Machine) to go from Windows-> Linux, Mac-> Linux or Linux-> Linux.
It is much faster than vnc or exporting (or rsh or ssh -X) back to my workstation display.
"Better to remain silent and be thought a fool than to speak out and remove all doubt."