I had a small air source heat pump integrated into the mechanical heat recovery / air system in my last house. The efficiency would drop off at below 6c with the expelled air being well below freezing point. This would cause icing up in the heat exchangers (as air temp dropped moisture would be released) which would kick off the reverse function (to melt the ice) which stopped the house heating

. In reality it really needed a pre-heat integrated which would keep the incoming air over 6c, this would have added substantially to the running costs as the heaters are just electrical coils. With a bit of work to the ducting I mixed the incoming air from outside with air from the loft (it was a warm roof) which helped keep the temp of incoming air a bit higher.
Not sure how the modern air source heat pumps deal with this problem, but at the time they started to incorporate pre heaters, which would negate any cost saving. Would be interesting to hear from those who have systems installed and monitor low temp costs?