Why heat pumps do not work as well in very cold climates as they do in milder ones. is the same true of refrigerators?

Heat pumps work by compressing refrigerant gas until it is hotter than the air you want to heat.

The hot compressed gas is then passed through a condenser (similar to the radiator in a car) and air is blown past it so that the heat is transferred to the air. This warms the room.

As the compressed gas is cooled by the air that it's warming it condenses to a liquid and then passes through a very narrow tube which restricts its flow and delivers it to an evaporator, located outside.

(The restrictor is needed so that the pressure in the condenser can build up enough to liquefy the gas).

The evaporator is made of larger diameter tube with fins around it (also made similar to a car radiator), which allows the liquid to expand and boil (it's now at low pressure again after passing through the restrictor).

The refrigerant is a gas which boils at a low temperature (usually well below #0^@#C at low pressures) and as it boils it gets very cold and takes in heat from the outside air, which is being blown past it.

The refrigerant, which is now a gas again at close to the outside air temperature, is then returned to the compressor, where it is again compressed and piped to the condenser (where it gives up the heat it just got from the outside air).

If the outside air is very cold, the amount of heat available is less than if it is warm, so the evaporation phase takes longer (more air has to be blown past) and the gas contains less heat (is colder going into the compressor), so the process does not work as well in very cold climates.

Fridges use the same principle but the evaporator is inside the fridge and the condenser (which gets hot) is on the outside. So fridges do not work as well in very hot climates because the condenser is not as well cooled.