Now, the whole point of having a heat pump is to have a COP (much) greater than 1 (an excellent furnace has a COP just below 1). Once the difference in ambientT-outsideT becomes large, you approach COP = 1. The heat pumps manufacture will report the actual COP vs $\Delta T$; that is including losses, vs theoretical.
Now, a heat pump runs (almost certainly) on main power, and the alternative (usually) on natural gas.
It's a simple matter, therefore, to calculate the CO2 and financial cross over point for a heat pump vs. a furnace. I did that calculation when I had one installed in my house (for ductless AC; heating is an added bonus). It's somewhere between about -5 or -10 C, if I recall correctly.
Sure, a heat pump can work at -25C but it'll cost more and emit more CO2. This is because, dumb Joule for dumb Joule, natural gas piped to my home is cheaper and cleaner than the same natural gas piped and burned in a thermal power station [1]
In my small corner of the world this means that the heat pump is usually better to run than my furnace. But I keep my furnace on anyway, basically set on idle because there is no way that a heat pump can compete with a furnace on reliability. I don't want burst water pipes.
In Europe, heat pumps make 100% sense. Even though Europe is significantly north of the US, the winters are mild with few stretches below 0. In contrast, in some parts of the midwest long stretches of -20 C are not impossible. A week at -20 is not unheard of. In this situation Id be loath to have to rely exclusively on heat pumps.
[1] actually coal in my case so I fudged it in favor of the HP. Coal is also the case for many of you as well because coal is typically used as marginal power during the winter since it's easy to store and gas pipelines' pressure drop in the winter due to home demand.