I have a heat pump. It does the heating and cooling.
I live about 1/3 of the way up from the bottom of the US. We do not usually have very many days where it gets below 15 deg F.
Heat pumps loose efficency below about 25 deg F. Around 15 deg F they are really poor and probably cost as much as resistive electrical heat to run. They usually have electrical heating elements in the inside duct work to help when it is very cold.
That is the reason that most of the Norther states where it gets to near zero F and lower the heat pumps are not used . It is usually more efficent and less expensive to use other forms of heat.
I have never checked the price but I would think there should not be much difference in a heat pump and plain air condition. I would install the heat pump and another form of heat.
There are some units called a gas pack. They have natural gas for the heat and electric for the AC.