If you heat with electric heat does it cost you more to leave the refrigerator door open during the winter since any lost energy goes into heat anyway?

Answer 1

The energy you put into running the fridge, which is that required to run the compressor, will in any case appear in the room where the fridge is situated, so if this room is in the house and not in an unheated outhouse where this energy would be lost, this energy goes towards the total you need to keep the house warm. You probably have noticed that the heat exchanger on the back of the fridge gets warm, and in fact it's best to allow some air to circulate behind the fridge to take this heat away by convection, so it does add to the heating in that room. If you leave the fridge door open, the compressor will need to run overtime, maybe even continuously, so you use more electricity for the fridge but this will help to heat the room. However the purpose of the fridge is to keep the contents cool, and with the door open you will get temperature gradients that mean part of the contents is not at the desired cold temperature, so it's not a good idea!

A somewhat similar argument can be made when using low energy light bulbs instead of normal ones. You put less energy into the lighting, but that must mean you need more energy from the heating system.