Mitsubishis can work down to -13F/-25C and still have a COP of 2.08:
* https://www.mitsubishicomfort.com/articles/keep-warm-this-wi...
* https://mylinkdrive.com/viewPdf?srcUrl=http://enter.mehvac.c...
Heat pumps that look like standard ACs often can run at 100% capacity down to 5F and still have a COP>2 (1=resistive heating).
Also worth perhaps looking into how leaky your house is:
* https://www.energy.gov/energysaver/blower-door-tests
and then after that maybe insulation.