A laundry or dryer appliance may include a cabinet, a drum, a transmitter power coil, and an additive dispensing assembly. The transmitter power coil may be mounted to the cabinet proximal to the door. The additive dispensing assembly may include a fluid pump, a receiver power coil, and a dispenser nozzle. The fluid pump may motivate a volume of a liquid additive therefrom for an additive mist to the drum. The receiver power coil may be in selective wireless communication with the transmitter power coil to receive an electromagnetic field therefrom. The receiver power coil may be operably coupled to the fluid pump. The dispenser nozzle may be directed toward the drum downstream from the fluid pump to guide the volume of the liquid additive into the space defined by the drum.