That very much depends on the cost of your electricity and fuel. In MA, where I pay about $0.20/kWh and around $1.60/therm (both delivered), natural gas is around 2/3rds the cost of a heat pump in the coldest months (and loses only slightly in the shoulder months, when the heat pump is more efficient but you don’t have as much heat loss).
Here are lab test results for some of the most efficient heat pumps on the market: https://www.nrel.gov/docs/fy11osti/52175.pdf
Below 25F the heat pump is more expensive. At 35F it is cheaper. (Page 10)
Natural gas would be about 2/3 cheaper at 5F.
There are "hybrid heat pumps" that might make more sense in your climate. They use resistive or natural gas below a certain temperature. I'm not sure which "side" of the compressor they heat.
No I'm not; I'm literally looking at my last gas bill right now. I'm paying $0.8309/therm for gas and $0.8945 for delivery services. That's $1.7254/therm, not $5.80/therm. (At $5.80/therm, I’d have upgraded a decade ago [or switched the house back to #2 fuel oil]!)
At 85% efficiency, that's $20.30 per million BTU for gas. *
Looking at the only maker of split-system air-to-water heat pumps in the North American market, their spec sheet COP** at 120ºF leaving water temperature is 3.33 at 45º outside air, 2.86 at 35ºF, 2.42 at 25ºF, and 1.99 at 15ºF. For February, that looks like I'd expect a BTU-weighted COP of around 2.5-2.6.
All from a system that would cost me around $15K additional out-of-pocket (after incentives) and would save a few hundred bucks in the shoulder season and cost me a couple hundred extra across Jan and Feb. $15K and less comfort on the coldest days to save $100 per year is a pretty negative RoI. $15K invested in Treasuries has a higher (and more certain) return and is liquid at the end, not thrown away.
* https://www.amsenergy.com/fuel-cost-calculator/
** https://www.nordicghp.com/wp-content/uploads/2021/10/001850S... (I selected the split-system here because it avoids the efficiency and temperature losses from a glycol-to-water plate heat exchanger that the monobloc units would entail. I need every degree of leaving water temperature that I can muster as I determined experimentally that my house is able to be comfortable down to 12º outside air temp at a boiler LWT of 130ºF on 1st and 2nd floor, but needed 145ºF in the attic [so would need to have the emitters [currently finned baseboard] replaced if I could only muster 120-125ºF LWT].) Spacepak is coming out with a split ASHP sometime soon, but has no technical literature published yet and I'm not going to be the first in the nation... :D
I studied the crap out of this, because I was hopeful that with $10K of incentives on the table that this could be close enough to make the switch worthwhile and eliminate on-site burning of fossil fuels in the house. It seems like we’re not there yet and there’s no guarantee that electricity will inflate at a pace slower than natural gas over the next 20 years, so this could get better or worse. Maybe the only supplier goes belly-up. Maybe something better comes along and no one wants to buy a house with this weirdo system in it. Parts would probably not be in stock at the nearest two supply houses. Only a few plumbers could work on it. In a scenario with that many unknowns, dropping in a $3K combi that everyone knows how to work on and parts are on the shelf 10 minutes away for $3-5K out of pocket (after factoring the almost $3K incentive on a high efficiency gas boiler) is a way better play and then see what comes along 10 years from now at the boiler mid-life or 20 years from now when it’s due for replacement.
You can use that number when looking at a heat pump's datasheet to see which temperatures the heat pump would be cost effective for you.
For me my electric rates are pretty high, and my gas rates are pretty lowso in the winter I doubt a heat pump would be cheaper, in the fall and early spring when you just need to raise maybe 10deg over outside sure, but in the deep of winter I doubt it