Hi Golden,
Welcome to the forums.
I did a "back yard" experiment on my water heater. The ten gallon unit cycles every four hours and it takes about 15 minutes to shut off again. That means in 24 hours of NO water being drawn the heater runs for 1.5 hours.
My conclusion was that it was best to turn it on until it reached full temperature--then shower. After the shower I turn ig off and there is enough water to rinse my hands, and do dishes for the day.
Another friend did a month long experiment where she left the water heater running--and the month after she turned it on only "as necessary". Her propane use dropped dramatically in the second month.
BTW have you looked into renting a larger propane tank for the winter?
You might also want to consider a Platinum Cat because it is inherently more efficient than the propane furnace. It is vented and has a thermostat.
Platinum CatI ran another "back yard" experiment two days ago starting with my RV at -20 C when the ambient temperature was -30 C. If you wish to see the results surf here:
Heating Electrically a "back yard" report