Not exactly true, one of the main issues with heat pumps in cold weather is the outside coil freezing up with ice blocking airflow due to them being below the freezing point of water.
This is actually why older heat pumps became less effective around 40F because the coils would start to hit 32F since they are attempting to pull heat from the warmer outside air and are therefore colder than the outside air.
There are various solutions to this problem, the standard way is to run it in reverse as a air conditioner for a short period if it detects the situation to defrost the coils and if the system has resistive heat strips it uses those to warm the air that is being cooled. This obviously reduces the efficiency of the system the more it has to defrost and may not be very comfortable to the users.
Cold weather heat pumps work better in drier climates due to this as well because the lower the outside humidity the slower frost will form on the outside coils.
Some cool weather heat pumps will have two compressor units and fans and alternate between them with one defrosting the other, there are many other tricks they are using to prevent frost buildup and continue working above COP 1 far below freezing.
