Yes, in a carefully designed system, and no, if you hang a mild-climate or undersized head and hope. A ductless mini-split that is also a cold-climate heat pump can be the only heat source in a cold climate when its heating capacity at the local design temperature meets the room or house load, and when the occupants accept that a power outage stops the heat (unless you have a generator plan). ENERGY STAR’s cold-climate criteria — a COP of at least 1.75 at 5°F and at least 70% of 47°F capacity, with a higher HSPF2 minimum for non-ducted units (8.5 in the criteria this site already cites) — are a useful floor for the machine, not a sizing calculation.
What usually goes wrong: sizing from a cooling rule of thumb, ignoring infiltration and glass, or skipping backup of any kind in a house that cannot go unheated during a defrost or an outage. Some owners still keep a small resistance heater or a wood stove as a last resort; that is a comfort and safety choice, and the resistance heater is a panel load if it is hardwired. See the backup-heat and backup-furnace pages for the larger-system version of this question.
Have a Manual J done at the design temperature for your town, read the capacity tables at that temperature, and confirm the circuit. The operating-cost calculator uses seasonal ratings and will not, by itself, prove the unit can heat the room at −10°F.
This is not a permit calculation, a utility approval, or a substitute for a licensed electrician, HVAC contractor, or the authority having jurisdiction. Panel Headroom is an independent educational site. It is not a utility, a certification body, or a contractor. Electrical and generator work that is done incorrectly can cause fire, shock, or carbon monoxide poisoning. Use the adopted electrical code and manufacturer instructions; pull permits where required.