To avoid heating expense we would like to completely shut down an unoccupied family home in Northern New Jersey. Can we expect the old plaster walls to survive the temperature extremes.
I would be hesitant to leave any house -- regardless of age, condition, or construction -- without heat over the winter. It is not the temperature extremes but the moisture that will damage an unheated house. The cost of repairing damage (mold and mildew are the most likely problems) can easily exceed the cost of heating.
You'll certainly want to winterize -- blow out pipes, put antifreeze in drain traps, seal any exterior penetrations (except where required for combustion appliances). The heat doesn't need to be much; 50 degrees will be sufficient to protect the home from moisture damage. I would be hesitant to go below 45.
Your experience will be different based on the part of the country you are in. I don't know what the climate in NJ is, but here in the Pacific Northwest the humidity gets extremely high during the winter rainy season, so mold can be a BIG problem. In the midwest, the humidity can get extremely low in the winter. In a low humidity environment, you may be able to get by without heat.
I've seen pictures of Alaska bush houses that have been abandoned for years, but look as if the occupants were living there yesterday.
Thank you "Fencepost". Articulate, first class advice.