They can function down to -5F at full capacity.
Heat pumps are fascinating. While resistance heating can have an efficiency of 1, putting out a KW of heat for every KW of electricity used, a heat pump can have an efficiency greater than 1. It does this by using the latent heat in the outside air. As it does its thing, the system will have coils outside that are colder than ambient air. Your outside system has a minimum working temperature. The higher the difference between the outside temperature and this minimum, the more energy is available in the outside air to heat your home.
Since you look ready to pull the trigger soon, here are some cautions:
The LV241HV4 you linked to has 3 performance points published for heating:
Outdoor 17°F (DB) / Indoor 70°F (DB) 26,000 BTU/h
Outdoor 5°F (DB) / Indoor 70°F (DB) 23,600 BTU/h
Outdoor -4 °F(DB) / Indoor 70°F (DB) 20,760 BTU/h
It's nominal capacity is 24,000 BTU BTU/h
It has very good heating, even at -4°F, performing at 86.5% of its rated capacity, but it does have a reduced capacity. (note this does not mean your system is
less efficient at -4° than it is at 5°, because you're asking it to work harder)
The other thing happening at colder temperatures is your house's heat losses are increasing. They are generally proportional to the difference in temperature. At -4°F, you have 13.8% more heat loss than you do at 5°F.
It's rather unfortunate that the performance of a heat pump goes down just as you need it the most, but that's physics. You can either upsize the unit from your normal conditions so you have adequate heating at the minimum temperature condition (but more heating capacity than you need most of the time) or you can add a resistance heater to help with those very cold, non-design days.
One last thing to note: You don't want to operate outside of the operating range. I wouldn't be surprised if the heat pump controls refuse to let it operate below -4°F, to protect the system from frosting. That would mean a hard no-heat cutoff at -4°F, unless you have some resistance heat.