A heat pump is most stressed when working in the coldest weather because the temperature is low and shutting the compressor off stops the heating of the oil in the system. Manufacturers often prefer that the compressor run during the cold weather to keep the oil warm and moving.
You will lose a bit of your savings by shutting off the compressor; however, there are in many areas a short number of days where the weather actually stays below freezing. Turning the unit to emergency heat for those months and keeping the compressor off so the compressor does not have to restart below freezing can be done to avoid this defrost cycle noise.