In our own research and calculations, which were supported by a vendor and PH certifier, we find that cold-climate (outdoor) air-to-air heat pumps (for space heating) in a Passive House in climate zone 6 and around 8,000 heating degree days currently achieve a COP between 2 and 2.5.
The way to beat low natural gas prices and get away from the CO2 source is to build Passive House, or EnerPHit, then add the heat pump and—very importantly—fuel it with carbon neutral electricity. That way you minimize cost and environmental impact.
Indoor air-to-water heat pumps (for domestic hot water heating) can achieve higher COPs as they utilize (70º F) indoor air to create hot water (so they steal it from Peter to give it to Paul). Those can be above 3.5.