Aeration is overall one of the best things for a pond, but having aeration during the winter months can change that. The way a pond works in the winter is the opposite of the summer. The warm water in the pond is actually on the bottom of the pond, and the cold water is on top. Running aeration too much in the winter can cause the cold and warm water to mix, which can be very stressful on the fish.
Below is an image that shows pond turnover.
We do not recommend running aeration in the winter, unless you have a winter diffuser along the edge of your pond, normally around 3 feet of depth or less. This is a safety factor with thin ice, and can also harm your fish. A winter diffuser is an air-stone that we offer/install for keeping a hole open in the ice for allowing sunlight into your pond, and for wildlife to have access to water.
Lastly, you want light to be able to penetrate the ice so that photosynthesis can occur to create oxygen in the water. This can be done by either pushing a section of snow off of the ice, or letting your aerator run just enough to break a hole in the ice.