Heat pumps don't work well below about 35 degrees, because the outside coil starts icing up and the pump has to use energy to defrost it. I
This is not really a valid statement. Modern heat pumps are generally rated to make twice the heat compared to electric baseboard at 17 deg F. Icing does reduce the efficiency, but icing is more a factor to the local weather. Rain, high humidity and wet snow can all cause icing, but cold dry air causes little to no icing. In reality the defrost cycle does not have a major impact on overall efficiency, since it is quite short term in operation. Modern heat pumps with demand defrost are quite good as the defrost occurs occur when needed, as determined by sensors.
The biggest factor reducing the efficiency of a heat pump is capacity loss. As it gets colder, the amount of heat (BTUs) drops as it gets colder, so a 36,000 BTU unit will generate 36,000 BTUs when the outside air is in the 40's. By 20 deg, the amount of heat generated may only be 20,000 BTUs, although those reduced BTUs are still made with 40% to 50% of the electricity that would be needed for an equivalent electric heater. Problem is that as it gets colder, the output drops. Colder also means the heat loss of the house is greater, so you would actually need more heat. So to fight the lower heat output and the additional need for more heat as it gets colder, the electric supplemental comes on, which does have an impact on the efficiency.
A modern, properly sized heat pump should not require any supplemental heat until the temps are in the mid 20's outside. Overall it is still pretty cheap heat.
Paul