Many manufactuers seem to offer warm and cold climate models. For example, pulling a random manufactuerer, Mitsubishi brands their cold climate line "Hyper" and specs out much better efficiency down to -13F temperatures.
Below 20F it puts out so so heat but can maintain. Below 10F electric heat is needed from time to time to maintain. Below 0F heat pump is worthless.
Edit: Wanted to add my is air heatpump, not ground source. Also reading other comments looks like heatpumps range from amazing to utter crap.
2. If it's not a coolant or compressor issue, you might need to replace it (either because it is undersized or end of life). Your local government or utility might have energy incentives for replacing it. There are also federal tax credit incentives [1].
[1] https://www.energystar.gov/about/federal_tax_credits/air_sou...
My heat pump in Iowa worked just fine to keep the house comfortable down to 14F (the system automatically switched to backup heat colder than that). Something is wrong with your system if it can't do that. I couldn't begin to guess what though.