UPDATE: I stupidly didn’t notice, until a commenter pointed it out, that this article talks only about air-to-water heat pumps, which do the harder job of heating up water to be used in home heating, rather than the more common air-to-air system. These conclusions should NOT be used for air-to-air heat pumps.
When I moved to New Hampshire in the late 1980s our apartment had an air-sourced heat pump and it really sucked – didn’t do a good job for many weeks in the winter. But the technology of removing heat from the air through compression and expansion of liquids has improved by leaps and bounds since then and heat pump fans say they are now a viable alternative here.
Sustainableheating.org has a small article looking at the issue (read it here) and says that air-to-water systems can carry the load when the air temperature is above 15 degrees F. Below that, things get iffy; below 0 F, they’re useless.
The above chart is from a firm called Appropriate Solutions.