Old house with thin walls, to insulate or not?

I am facing the decision of whether Grandma's old house should be insulated from the outside with Styrofoam or not. The house is old, built in 1929. Inside everything is new, only the outside is not, hence the consideration whether it should be insulated right away or just plastered. In winter, the unheated rooms get very cold, the exterior walls including plaster are only 18 cm thick, is that typical for the year it was built? Therefore, insulation would actually be a good investment, although I don't know if there would be a noticeable difference after thermal insulation, what do you think? In winter, not all rooms are heated around the clock, when you enter an unheated room, it is very cold. Now we are wondering what the difference would be if the house had thermal insulation.

The house is old, built in 1929. Inside everything is new, only the outside is not, hence the consideration whether it should be insulated immediately or just plastered. In winter, the unheated rooms get very cold, the exterior walls including plaster are only 18 cm thick, is that typical for the year of construction?

18 cm with plaster is not typical for the year of construction, but rather an indication of a wooden structure. For stone, I would expect a wall thickness (raw) of 25 cm for this year of construction.

I would clarify the wall structure first. What about the windows? - surely the roof is not insulated either. When was the heating renewed, and when the water pipes?

1929 does not spontaneously sound to me like "if it is insulated, it is up to date and in good condition." What exactly is "everything new inside"?

The windows were replaced with new plastic windows, the roof was also re-covered, including insulation, otherwise everything inside is up to date, meaning boiler, water pipes and lines, radiators, etc. The walls are made of stones, they are gray stones, I don't know what they are called. Whether there is also wood inside, I don't know. On the wall, there is a wooden construction, on which panels were then attached, they look like plasterboards, and in total (including plaster) they are 18cm.

Can there be concerns about insulation with this construction method? Is it advisable at all?

the windows were replaced with new plastic windows,

During the installation, one must have seen what the walls are like.

The walls consist of stones, they are gray stones, I don't know what they are called. But whether there is also wood in between, I do not know. There is a wooden construction on the wall, on which panels were then attached, they look like plasterboard, and overall (including plaster) it is 18 cm.

pumice stone is coarse-grained, the color of cigarette ash, rarely somewhat more earthy, and at that time small stone formats. Aerated concrete ("Ytong" / Hebel etc.) is light gray to cream white, is often processed in large formats and very often used in timber frame renovations - also because it can easily be sawed into any shape and thus fits well. For timber frame buildings - which at that time were very often completely plastered, i.e., not designed as exposed timber framing - it is common practice to "straighten" them during modernizations using battens and plasterboard.

18 cm is an absolutely unusual thickness for masonry walls. Stones back then had a length of 25 cm and a thickness of 12 cm. Since exterior walls were never built only with stretcher bonds, a stone length practically already determined the thickness of a wall. In the Adenauer era, the stone format was changed to 24 cm length and 11.5 cm thickness. Only in the 1980s did they start to process very large stone formats (half a meter long and a quarter meter high), also to build exterior walls only with stretcher bonds (i.e., without layers where stones lie "crosswise"), and for that to manufacture stones in all usual wall thicknesses.

In timber frame renovations, flat aerated concrete stones in thicknesses of 10, 12.5, 15, 20, or 25 cm were gladly used. Timber beam thicknesses around 1929 were probably already most commonly in metric measurements (so no longer inches) of 12, 14, 16 cm. Later, aerated concrete stones were placed into the infill panels as a replacement for loam-coated willows. For exposed timber framing, starting from the beam thickness the next thinner size was used and then plastered; for plastered walls, the closest thickness and made "level" with battened plasterboard panels.

Your stated total wall thickness clearly argues against "masonry" and is highly suspicious for "timber framing". This should be clearly visible on a thermography.

Non-load-bearing interior walls at that time would have been executed with 12 cm masonry thickness if the house was masonry. For interior walls purely for room dividing function, both in masonry and timber frame buildings "rabbit walls" were common; in masonry buildings partly also those made of stones laid on the narrow side (i.e., 6.5 cm thick).

Can there be concerns about insulation with this type of construction? Is it recommended at all?

What to insulate with and when better outside or inside will have to be clarified with experts. Before that, it must be clarified how the wall structure is. During window installation, one must have already seen a lot about what kind of wall it is. And thermographies help with that as well: the beam pattern shows through clearly.