Fellow midwesterner here. The last time I looked into it, heat pumps were significantly less efficient in cold temperatures. Is that still the case?
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.)