"Can keeping a room unheated cause plaster damage?"

Yes.

Warm moist air coming into contact with cold plaster can case condensation.
It can be on the finished surface or on the back of the plaster.

I have never noticed more pronounced degradation in the plaster in unheated rooms in my house compared to the heated ones. (My mid-19th c, northern NY, house -with all rooms retaining the original plaster intact - has no central heat. As a consequence some rooms are completely closed off in the winter to conserve warmth from the wood-fired heating stoves. This means some of my rooms are steadily near, or below, freezing all winter; this peculiar "winter" being the exception in a quarter-century's occupancy.)

Are you sure the plaster in that room is of the same vintage as the rooms you are comparing it with? Perhaps it was a later addition or renovation made with different materials.

Are the cracks small, relatively straight, hairline ones running with or at right angles to structural members, or lathing? If so, you might also consider doing a careful inspection of the building's framing to search for a localized area of rot, pests, or inherent weakness that is expressing itself by allowing sections of the plaster to flex and crack.

If the paint is peeling, I would consider it possible that a poorly done, or calcimine, or incompatible undercoat was the culprit.

HTH,

Liriodendron

Thanks for the help! The cracks go every which way and don't run at any angles, least of all to the windows and doorway thank goodness. I will have to investigate the condensation angle. In fact, the trap door to the basement is in that same room, and the basement has quite a lot of condensation (we're working on fixing that.) I wonder if that has something to do with it.

My pantry is unheated, and the register is on the other side of the kitchen from its door--which stays open all year long since the refrigerator is in there. I have never had problems with the plaster cracking or crumbling in there, though the wall is covered with painted paper.
The walls have blown in insulation, and there are some batts stapled between the floor joists which sit above a crawlspace outside the house foundations. The pantry faces east, if that makes a difference.

Can the wall be damaged if it is unheated and the rest of the house is?

Yes.

Does it happen every time? No.

If the entire house is unheated the risk is lower, but moisture from heated portions can get into the unheated area and sometimes causes damage.

It is very site specific.
If you are worried the only test is to try and see what happens.

My "unheated and closed-off rooms" are definitely not isolated, unused spaces. I sleep every night in one, for instance. Another is my back entrance hall (a sort of mud room, but this being a farm it is unusually large) which in warmer weather is always open to rest of the house, but in winter the connecting door is kept closed (and is tightly weatherstripped). Except for the many times each day we go through it on our way in or out of the house, or to go further on into the wood storage room (wood heated house so that's at least 10 times per day.)

My sleeping room is on the second floor above heated rooms below, but the back entrance hall is directly over a dirt-floored crawl space (uninsulated and non-vapour-barriered) with a trap door in the floor opening directly to the open, stone-sided, well. Other closed-off rooms are intermittently opened (say before a party or before the holiday gatherings) but some stay mostly closed all winter (store rooms and my sewing room, for example). There are also other rooms, which without direct source of heat (no stove in the room) can get quite chilly but are not closed off by a door.

In any case I don't really see any difference that I would ascribe to temperature variations among the spaces. Perhaps it's due to the age of my buildings, the plaster thickness (my walls are back-plastered twice within the wall behind the three-coat on wood lath interior finish), the complete lack of wall-cavity insulation, or the nature of my climate.

I am always wary of blanket statements that purport to cover all old houses, in all areas of the US and of dissimilar age and construction.

Peeling paint in old houses can be caused by the paint, especially if there is calcimine in one of the layers. Resolution is removing all the paint and starting over with a clean, dry, sealed surface. But before you do that, pay some attention to the cracks themsleves.

For plaster cracks one of the best things to do, in my experience, is to take a pencil and draw a line several, or many, places straight across the crack and at the extreme ends of a crack. Write the date of the mark on the surface and observe for many months. Any rapid shift of the lines or extensions is worth paying close attention to. In my case every worrisome "new" crack has invariably turned out to be one that remains stable for years, and probably had been there for decades but never caught my eye before. It's very reassuring to directly observe no progression. One less thing to worry about in your old house.

HTH,

L