Yes, there are cold weather heat pumps that can thaw the coils to keep operating. There is a point where they just can’t continue to operate.

When I design a heat pump system in cold climates, I always include a secondary hear source that kicks in if the heat pump gets overwhelmed. Might be a gas section in a furnace. Might be an electric heater in a fan coil. Might be electric baseboards or wall heaters.