Not really. Heat pump is not creating heat unlike resistive heater. It's just transporting it. One must remember even though freezing temperatures are cold for humans, for physics and universe those are still relatively high temperature environment. After all 0 Celsius is 273 positive Kelvin degrees. So that is 273 Kelvin forth of heat to pump around. Well say in -30C, still 243 K worth of heat to pump around. So the issue isn't is there heat, the issue is the practical mechanical and thermodynamic realities of he pumping. Which in practice comes down to can you find suitable refrigerants with suitable phase change characteristics to pump around.

Which for normal ambient temperatures on Earth is "yes". Just usually matter of how high pressures one has to use and other nasty features of the materials. For example recently even just CO2 has been started to use more again, issue with it mostly being it has to operate at higher pressures than more traditionally used refrigerants. They just don't call it CO2 in the bizz, it's refrigerant fluid R744. That works down to -56.6 Celcius given its triple point temperature. So it won't heat one in antarctic -80C winter, but for most of Earth even in cold climates -56.6 C is plenty. Problem just is it has to always work under high pressure, since in ambient pressures CO2 just sublimated from solid to gas. Pumping around solid blocks of dry ice isn't very convient for continuous heat exchange process machine.

Which adds some cost to the pump components. On the other hand... CO2 is pretty darn harmless. As long as concentration locally isn't too high, humans, animals and plants are perfectly used to handling the gas they exhale. It is non flammable, it is green house gas, but it is green house gas we naturally exhale. Some unit leaking it doesn't change much, since usually CO2 for industrial use is extracted from waste product gas, that would end up in air anyway.

Plus on need be it can be distilled from air, it's just energy intensive. Which is why "carbon capture" isn't a bigger thing. We know how to do carbon capture. It's just energy intensive and thus on climate impacting massive scale energy prohibitive.