Can I save energy by putting my refrigerator or freezer outside in the winter?

NO. It won't help in saving either energy or money. On the contrary you may have to spend more as the food in the fridge will be spoiled or the compressor of the fridge will stop working. You can put the fridge anywhere if the room temperature is above 0 degree F.

Gases get hotter when you compress them. When you expand the gases it occupies more volume. When you have two things at a different temperatures near each other, the hotter surface cools and the cooler surface heats. Based on this principle refrigerators are working. So the room temperature should be above 0 degree around the fridge.

When the atmosphere temperature in the surrounding of the fridge is below 0 degree F , your fridge will get confused and it doesn't switch on the compressor as it should be in normal circumstances. So inside fridge the temperature is not maintained at required level. Which in turn cause your food to spoil.

If you leave your fridge outside the house, the dust will pile up in the fridge and motor will burn up soon. Even if you keep the freezers outside, the energy and money saving will be minimum only compared to the cost of repairing if anything goes wrong while you are shifting.

No. it does not matter what the climate is outside.