I'm curious as to how low a temperature your heat pump will operate. I live in New England and replaced a whole-house air conditioner with a heat pump, but the heat pump works only to 35F. Much colder than that, and an auxiliary electric heater kicked in. The first Winter cost me about $800 over my gas-fired forced hot water heating system. I had the contractor disable the electric heat in the Spring and rewire the thermostats to start the (high efficiency) furnace when the outdoor temp got too low.
Keep in mind that heat pumps have a limit how much they can pump (it also depends on temp., there is less heat in 35F air). If your house is not well insulated, at a lower temperature it would be loosing more energy and eventually it would reach the threshold where it's performance is not enough to keep up.