Yes, no problem here in DC. People who had or are having trouble probably aren't lying, but they likely have much older systems, are remembering an experience from years ago, or got the wrong type of system installed for their area. Current technology works much better in cold temps than old systems did, as long it's the right type.
https://www.consumerreports.org/heat-pumps/can-heat-pumps-actually-work-in-cold-climates-a4929629430/
"When properly installed, plenty of today’s air-source heat pumps (simply “heat pumps,” for the rest of this article) can keep your home toasty even amid bone-chilling cold, using far less energy than other types of heating systems. ... Derek Traxler, a computer repair technician from Minneapolis, told us that after his steam boiler broke, he installed a heat pump that has kept his home warm for the past four winters, including during extreme cold snaps, when temperatures dropped as low as minus 29° F.
the NEEP, Lis’ organization, maintains a database of heat pump models that will perform well in cold weather. Many models in the database can heat as effectively at a frigid 5° F as they can at a mild 47° F, and can also work pretty well at temps well below zero. In other words, these heat pumps are built for the big swings in temperatures that the Northeast and Midwest see every winter."