My mom used to talk about the clothespresses they had in various homes when she was growing up. Those weren't for airing, per se, as I understand it, but for actually pressing, i.e. ironing the clothes or at least keeping them in a neat fashion after ironing. I've seen them in old colonial house back East, quite often right next to a fireplace. They have a ordinary looking door, but when one opens it, the depth to the back wall of the "closet" is only a few inches. One would hang their clothes there, shut the door, so that it compresses the clothes.
I like the sounds of the airing cupboards, but in the dry, dry West we'd have no need. No humidity to speak of and lots of sunshine to dry things quickly.
I found all kinds of places for sale in the UK that listed airing cupboards and/or hot presses, but no piccies, except for one of a young man who'd gone to sleep in one after a late night at some apparent school!