During the winter, my heat pump delivers warm, but not hot air and will seem to operate for long periods of time. Is this normal?

Yes, this is typical for a heat pump. Heat from a heat pump does not “feel” like a gas forced hot air furnace or a hydronic system with radiators or baseboard heat. While those systems deliver a “warmer”-feeling heat, a heat pump will provide a more even heat delivery. It feels “cool” because it is cooler than the other heating systems mentioned, and your hand is closer to 98.6°, not the 80-something degrees that a heat pump produces at a register in your room.