They just turn off certain devices, not the whole house. They can turn off just the water heater for no more than an hour at a time and they rotate the outage across their customer base. My large water heater tank ensures we’ll have hot water available.
I also have a “dual fuel” furnace, which can heat with either electricity or propane. During peak periods they can turn off the electric heat for an hour or so, in which case the furnace switches to propane.
In return for allowing the cooperative to control my water heater and furnace I get a lower cost per KWH. During this past winter I paid about $.071 per KWH for heat. I have two electric meters and my rate for other stuff (lights, cooking...) is higher than for the furnace and water heater.