We're building a house in Wisconsin soon. We think that ground-source geothermal is required for efficient electrical HVAC without gas, but if we can save a ton of $$$ and go with air-source heat pump, that would be awesome.
I ended up going with air-source heat pumps rather than geothermal. The geothermal units were less expensive, but the drilling was massively expensive.
Air source heat pumps now work down into pretty cold temperatures. With a high-efficiency air source our average heating/cooling bills are around $250 (down from ~$400 with older models). Even if ground-source got that down to $200, the payback period of the drilling would exceed our expected time in the house.
We still kind of wanted to do it, but the added problem was that no one in the area was really experienced with ground-source installs. So we would be dealing with the hassle of trying to get these HVAC guys to work on projects that they are not that interested in.
In the end we went with air-source, and it worked out very nicely.
Of course space heaters are far easier to move around the house compared to a mini-split system and would use less power if you only plan to heat a small room.
* https://www.mitsubishielectric.ca/en/hvac/professionals/fs-s...
* https://www.mitsubishicomfort.com/articles/what-is-a-heat-pu...
* https://www.fujitsu-general.com/us/residential/benefits/year...
Some folks using them in Alaska:
* https://www.nrel.gov/news/features/2021/even-in-frigid-tempe...
If you get a heat pump that looks like the 'traditional' external AC unit (giant cube), those tend to work down to about +5C. Not sure how much more they cost above a 'regular' air conditioner:
* https://www.lennox.com/products/heating-cooling/heat-pumps
The Technology Connections channel has a couple of interesting videos on the topic of heat pumps:
* https://www.youtube.com/watch?v=7J52mDjZzto
* https://www.youtube.com/watch?v=7zrx-b2sLUs
He has a video entitled "How to calculate when heat pumps make financial sense (and other heat pump follow-up thoughts)":
* https://www.youtube.com/watch?v=BRdq2ExLJns
NR Canada has a "AIR-SOURCE HEAT PUMP SIZING AND SELECTION GUIDE":
* https://www.nrcan.gc.ca/sites/nrcan/files/canmetenergy/pdf/A...
Financially speaking you're going to have to break out a spreadsheet and plug numbers in: (natural) gas prices, electricity prices, efficiency of the units, etc. Doing a search for "heat pump calculator" may get you started.
https://www.nrel.gov/docs/fy11osti/52175.pdf
I walk through the "what's the break even temperature" elsewhere in this thread (where I pasted the same URL).
Also, it is kind of a moot point. If you're putting in central air (not a minisplit), it will probably automatically fall back to natural gas or resistive if it gets too cold outside. (Too cold should be something like -5F or less, assuming it falls back to resistive.)