I start with a putty connection to my Linux box logged in.

Then on win, I start the cygwin bash shell.  From that I do an ipconfig to get my win ip address. From there it's

X >/dev/null 2>&1 &    (the trailing & keeps X in the background so you can do the following)

export DISPLAY=127.0.0.1:0
xterm &

then in the xterm
xhost <your linux IP address>

Now on the putty term I do a:
export DISPLAY=<win box ip address>:0    (note the colon zero)

and lastly

gnome-session &

This last you might need to replace with your KDE session manager if you swing that way, or whatever other desktop manager you use.

There are some annoying background processes I sometimes kill, sometimes I merely ignore them.

I've tweaked my desktop setup a bit for compatibility.  Since win pre-empts alt-tab, I've set ctl-tab to swap between windows.

I haven't had much experience going the other way.  We did have radmin at work.   It was evidently a very old version and on the server it was a hog crippling the box.   We're using vnc now.

-- TWZ