Windows has its own home baked VNC like protocol called RDP (Remote Desktop Protocol) – I love standards there are sooo many to choose from….! RDP is usually only usable from the so called professional versions however there is a way to enable it with the knobbled versions of windows.
First grab the RDP wrapper library from github
there is a batch file to install it an it basically just works without drama (which is always nice)
On your Linux machine you need an RDP client I used freerdp as my user name on both boxes is the same I only need to enter by password when logging into windows
xfreerdp /w:1366 /h:768 /v:192.168.0.5
as my screen resolution is larger than 1366×768 I get a convenient window with which to maintain windows.
one thing you should probably do it only allow connections from the local network for remote connections local port 3389 on the windows box.
While you can be sure of iptables rules, the window firewall GUI is somewhat confusing and its not always clear what the rules are actually doing, so you may be better blocking that port on your router just to be sure…