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Nice heavy curtains (which "pool" on the floor as I believe it's called when it's a fraction over-long to really stop draughts) are honestly brilliant at stopping draughts and insulating a doorway/window. We've got one across the kitchen doorway as the kitchen is a total heatsink and it makes a very noticeable difference.
Also obviously a lot cheaper than a new door (although making sure the door seals decently is worth it, just some new foam or stripwood around the edge can help massively) and you can easily take it down in the summer if required.
Our hallway is colder than a polar bears tits.
It's not like we need it heated, but we can't really isolate it from the rest of the house, and it's just sucking heat away.
I guess options are to get a new front door & transom (currently solid wood & single glaze) - which would be both expensive & fugly (if we went with an insulated / synthetic material).
We could put a doorway, but that feels like it would be a windup pretty quickly.
Would a heavy curtain just be a bit too Parisian bordello?