Out flat in Edinburgh New Town had built in shutters on the inside of sash windows - these were actually really effective at helping to keep the place warm - far better and easier to care for than curtains.

Edit: I should point out that the Edinburgh New Town is quite old, but not as old as the Old Town, obviously.

But wouldn't that be an apples to oranges comparison because shutters are fully opaque while curtains are only partially opaque?

I would also expect outer shutters to insulate the window a little bit and thus limit the heat loss no?

"curtains are only partially opaque"

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).

Indeed that's what I'm thinking about where the curtains are open most of the day but the net screens are always closed.

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.

Yes. And if a window is broken long term (who knows what 1000 years may bring) the opening can be somewhat protected still and easily so.