No the heated seats do not affect your fuel economy.
The heated seats do not cause your vehicle to use more fuel and the heated seats are a wonderful thing to have in your vehicle especially when it's cold out.
The way heated vehicle seats work is by use of an electric heating element which is a long strip of material that functions as a resistor.
A resistor resists the flow of electricity.
When electric current flows through it, the energy is turned into heat, which flows through the seat to warm the person sitting in the seat.
The heated seats use the energy from your battery and alternator but not use more fuel.
The heat that actually heats your car comes from the heated coolant that your engine heats up and then flows through a heater core and then gets blown into the vehicle through use of a blower motor.
The heat in your vehicle also does not use any more fuel.