I hate to say this but it depends: in the past, not so much as they were just modified A/C units Toyota has a dual phase heat pump that sounds like it handles lower temps better Tesla has the class leader with a multi-phase system I don't have ready access to my sources but Mr Google should have credible data sources. Bob Wilson
How far below zero are you thinking of? The below zero winter temperatures in Seattle are going to be a lot warmer than the below zero winter temperatures in Calgary AB.
My personal experience with the heat pump in my MINI Cooper SE is the heat pump stops being effective at about 20 ºF/-6.7 ºC. At around that temperature the amount of warming is negligible and resistive heating is needed. My car automatically switches to resistive heating when necessary, so I can't really confirm when it cuts over. But that's the temperature when I observe a noticeable effect on the vehicle range due to cabin heating.
Theoretically it should work just fine. At -35F temps and lower, the vehicle simply does not have enough insulation from the glass. If you have already factored in the 50% winter range loss then you should be fine!
Mini works down to -20C Note that by works what they mean is that the efficiency drops to 100% (ie same as resistive heating so no benefit over it). Above that efficiency improves to about 2-2.5x at temps above freezing.
MINI is a water/glycol heat pump with an auxiliary resistive heater and I believe Tesla utilizes a cabin water/glycol transfer plate (on the chiller & condenser) tied to the R-1234yf refrigerant octovalve system for the battery/motor/cabin. The downside for Tesla is the refrigerant at low temps will have reduced PSI for the boiling/condensing point below 14F or -10C (efficiency takes a nose dive). That and winter highway driving can cause some serious issues. I can't find much information on water/glycol 50% mixtures for comparison.
I have a 2021 Kona BEV with heat pump for cabin heat and battery heating and I am pleased with its performance. I live in the BC interior and I see temperatures down to about -20C. The car heats up quickly and stays warm. The more significant advantage of a heat pump, in my opinion, is the effect battery heating has on wintertime range and charging speed. Before I bought the Kona I drove a Bolt. Two roughly similar cars, but the Bolt did not have a heat pump or battery heating. At any temperature below about +10C the Bolt's range dropped off, and got rapidly worse with decreasing temperatures. IIRC at -20C the Bolt might only have 180km or so, while the Kona still has 300km. And the Bolt seemed to take forever to charge at those temperatures. At -20C a road trip in the Bolt required 1 hour of charging for every hour of driving (ugh!), not so in the Kona. The Bolt did have its strong points (a little roomier and I liked the driving dynamics), but I would trade those 10 times over to get the heat pump. Bottom line: if you need snow tires where you live, get the heat pump.