Modern ones will work very low and have resistive backups if it's really really bad.I had an air source heat pump in my old house.
Below a certain outside temperature (minus 2 c?) they won't work on heating cycle.
Which is obviously when you really need them to.
If they can work in Sweden (with properly designed buildings and selected heat pumps) then they can work here (with properly designed buildings and selected heat pumps).
The heat pump - a Swedish success story!
The sale of heat pumps has more than doubled in Sweden in the last 14 years - there are now 1,7 million heat pumps installed in the country that has 10 million inhabitants. At the Arena for Sustain
heatpumpingtechnologies.org