Why do you need shudders for your windows? Is that for hurricane/storm protection?
Edit: I should point out that the Edinburgh New Town is quite old, but not as old as the Old Town, obviously.
I would also expect outer shutters to insulate the window a little bit and thus limit the heat loss no?
Not any curtain I've ever encountered - people used to have net screens for privacy and curtains for warmth. But that's going back a bit (i.e. my youth).
It is still a decently common practice in a lot of European countries.
Other option would be to use rolling window shutters on the outside.