Heatpumps have an electric strip heat very much like the heater in your dryer that engages when the heat pump cannot keep up fast enough or when the difference between the actual inside temp and the thermstat set temp is different by more than a few degrees. Its pure electricity, like heating a stove eye or a water heater element. The bottom line is that since a house weighs so much, heatpumps tend to work best once the mass is at a given temp, say 68, and the machine only has to handle the energy to heat the weight of the house up one degree instead of many degrees.

This debate is old as when first comfort system was installed. Assuming you have resistant heat,,lowering either or both save's energy. Turning them off save's more even if outdoor temperature fall's to 33 deg . BUT,be sure to consider possibility of frozen plumbing if outdoor is expected to fall below 33 deg. If you have heat pump,there are variables which make accurate evaluation impossible without being on site.

Aside from water pipes getting too cold, if you keep the setting at 55 degrees or so as a minimum you shouldn't have to worry about pipes freezing, provided the pipes are properly insulated.

An old model heat pump will not perform as well as a recent model. The technology has made vast improvements from older machines. So I agree with klem1 in the number of variables it would be impossible to come to any real conclusion. Also climate can dramatically change the parameters such as "a heat pump buried in snow" versus "a heat pump that is not"

If you have the minimum setting of 55 to protect pipes and the comfort needs of the area are met then that's all that matters. Just realize to warm this area up, depending on the load (how cold it is) will take longer, than if your minimum setting is set at a higher temperature.

As far as how much you save or how much you don't... You don't burn energy if something is off. With that said, given the pipe freezing issue how much you save would depend on how cold it gets and how much the heater runs. These are variables that vary... if you can stand the pun. ;-)

My suggestion with the mudroom wallheater would be to turn it down as well. Personally, I'd probably leave it down (not off).

There are heatpump thermostats out there that can handle setbacks in such a way that it does not activate the auxiliary heating when recovering from the setback. It will have determined how quickly the system can raise the temperature (from experience) and will compute when it has to start in order to reach the desired temperature at the desired time.

I should have mentioned, no heat pump. electric furnace and then the wall convection heater in mud room on ground floor. No one is on ground floor after 9:00 pm.

In that case (resistance heat), lower the heat at night as much as you can. Turning it off for 8 hours or so generally shouldn't result in sub freezing temperatures inside but it all depends on the outdoor temperatures and the insulation. Turning it down to the mid 40s - 50s should be fairly safe.

If you visit Comfort Monster Heating and Air, they feature a number of tips for lowering your energy bill. Besides lowering temperature during the nights, a lot of it has to do with what heating system you're using, what type of Fuel, etc.

My Carrier Heat Pump and Thermostat do not call for backup heat when "the heat pump can't keep up". Additionally, not all heat pumps use electric resistive strips for backup.