A furnace makes heat. It burns natural gas and turns the chemical energy in that fuel into warm air. A heat pump does something different. It collects heat that already exists in the outdoor air and carries it indoors. That sounds impossible in January, and it is what trips people up. Heat is just molecular motion, and 30 degree air still holds plenty of it. Thirty degrees Fahrenheit sits roughly 490 degrees above the point where molecular motion stops entirely. A heat pump gathers that low grade heat, concentrates it, and releases it inside.
You already own one. Your refrigerator is a heat pump. It does not make cold, it pulls heat out of the food compartment and dumps it into your kitchen, which is why the coils behind it are warm. An air conditioner is the same machine pointed at your house. A heat pump in heating mode is that identical machine run in the other direction, pulling heat out of outdoor air and releasing it inside. Once you picture it as a pump rather than a heater, the rest of its behavior makes sense.