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Seasonal energy efficiency ratio - Wikipedia, the free encyclopedia says :
when a heat pump operates near its most inefficient outside temperature, typically 0 °F (−18 °C), the heat pump will perform close to the same as a resistance heater.
Lower temperatures may even make a heat pump operate below this threshold, which is why conventional heat pumps include heater coils or auxiliary heating
i suppose if we ever see single digits here again i would be advised to enable the auxiliary heat.
the way i under stand the machine works is that when sensed temp falls a small # of degrees [3 ?] below the set or demand temp auxiliary heat is engaged.
i have the aux. heat disabled with software/hardware because the resistance heat elements are quite large , 3 banks .
i choose to let the heat pump struggle to maintain demand in winter w/o aux resistance heat . i now learn that this is not an economic decision when the temp falls below a critical temp. .
to return to the OP question . if the space heater is to be used on *the coldest days* and those cold days are below 0F resistance heat would seem to be the choice.
in my cold basement i have a quartz type radiant in the laundry area. it is nice since when turned on and one is in font of it it is as warm as a roaring fire. the downside is that these types of units are less safe than others and if not monitored a roaring fire might ensue.
..a good safety unit such as the oilfilled radiators would be more appropriate if continuous unmonitored usage is desired