Have to be careful of condensation, and during freezing spells you want warmth to prevent pipes freezing.
Will lower temps damage a house? When I'm home alone in say November, my heating is off with a dehumidifier on. Do this every year, nothing has fallen apart and there's no mould.
But from what I've read, the general consensus is to keep a home at a minumium of 14C to prevent condensation.
And if you are elderly just stay warm and comfortable for your health.
Check the walls for damp in your laundry room, if the walls are 'sweating,' try a dehumidifier in there. A relative doesn't have a rad in the downstairs bathroom, 3 bed semi. Leave the door of the bathroom closed in winter, the walls get covered in condensation. Leaving the door open and running a dehumidifier, solved it.
When I was looking for a house, I'd see long term unaddressed condenstation destroy window frames.