If it is too cold and the fish eat, the food could ferment in their digestive tract and kill them. In the winter with power off, the temperature will drop lower and the lights will be out. Usually most fish will not want to eat if they are cold and in the dark. If you feed fish and they do not eat it, then the decomposing food can pollute the water to dangerous levels as well. In the summer, the fish may want to eat but do not give in.
Most fish can go at least a week without any food.
In heavily planted tanks, fish can survive even longer by eating microorganisms, leftovers in the substrate, and the plants themselves. Hopefully, the tank is already in a location that receives some natural sunlight and no move is needed. Taking the plants out also takes a potential emergency food source from the fish. If the power is off for more than a day, the tank's pollutants must be diluted, and the tank may have to go through the nitrogen cycle again. Even with days without power, the filter should retain some bacteria to restart the colony.