Extremely well taken points. I am trying hard to move everything to Arch and make myself as independent of Windows as I can. From what I understand, I should install
vncserver -geometry 1440x900 -alwaysshared -dpi 96 -localhost :1
on the server, and then I can log into it from Windows with a generic VNC client.
This seems more attractive that tunneling X11 through Putty and Xming which is quite messy in my (limited) experience. I will try that!