As I said before, there are many variables. In a home with lots of windows or standard insulation, I'll agree that below freezing temps will cause those HP's to struggle. Another variable is what indoor air temperature are you trying to achieve? If you are trying to maintain greater than 70 degrees when it is below freezing, you will need supplemental heat. A heat pump will never achieve the warm air temps at the supply vents a gas furnace will.
If you allow your ambient temp to drop, say overnight to 60, then in the morning you want to raise the temp to 68 with OAT's below freezing, you are going to need strip heat. If you want to achieve a stable 68 degrees continually, you need to "set it and forget it". A well installed HP can "maintain" a comfortable IAT well below freezing. It cannot heat a space as fast as gas. If you have kids running in and out of the house leaving doors cracked, you will need supplemental heat.
I installed my heat pump up in my home to operate in three stages. It is a 10 SEER 4 ton heating 2200 square feet with at least 1 return in each room. Now I have seen builders put 3.5 ton units and smaller in homes this size with only one or two filtered returns. Your duct system makes a massive difference in system performance. Those small HP's will not heat as well as my 4 ton. When the summer OAT approaches 100, these small units will not cool as well either. Manual J allows for up to a 25% size increase over the cooling load for HP's.
Stage 1: Heat pump only with 1 degree temp drop.
Stage 2: Heat pump + 10K strip heat with 2 degree drop.
Stage 3: Heat pump + 10K + 10K with greater than 2 degree drop.
The stages drop out in the same order. I set my system up in this manner because when I want heat, I want heat now. I like to sleep a little cooler at night and bring it up in the morning. 99% of the time, once I have achieved 68 IAT, the HP will maintain it. Electric bill runs between $150-$200 a month.
Now, I retract my statement about HP's maintaining IAT's in the teens. Temps that low rarely happen in Georgia, so I have little HP experience below the 20's. I can say, however, that my HP has done its job for the last 6 years.