Now if you are allowing or forcing the backup (Emergency) heat to kick in yeah that will blow your electric bill to the moon, even dipping down in the teens here in Atlanta I don't ever recall seeing my Nest calling for the backup heat strips to kick on. IDK your system though so just passing on what I know - your climate is prime for a heat pump though.
Some of the slack-jawed yokels that pass as HVAC technicians in some places think that the heat pump should be locked out below 40F and only backup emergency strip heat used below that temperature.
And I think some of them actually go as far as to add an outdoor thermostat to make sure only strip heat is used below 40F.