This article should answer your questions and ease your mind. Fish are pretty easy to care for in the winter. Being cold-blooded, their activity level drops along with their metabolisms. During the cold season, they'll spend most of their time resting safely at the bottom of the pond where the water is warmest. The only things they're counting on you to do is ensure their pond stays oxygenated and doesn't completely freeze over. Some ice is fine, it adds a new dimension to the pond that will evolve throughout the season. You just have to keep a small hole open in the ice so unwanted gasses can escape the water.
The problem with the entire pond freezing over is that the gasses released by decomposing organic matter at the bottom of the pond then have no way to escape the pond, which leads to toxic levels of these gasses building up in the pond. Fortunately, preventing that from happening is as simple as maintaining a hole in the ice. This can easily be accomplished with the proper application of heat and aeration.
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If you have a waterfall on your pond, you should be able to run it year-round with the right pump. Pumps that move at least 2000 gallons per hour should be fine to operate throughout the winter. A waterfall in the winter will create beautiful ice formations and add a fun new dimension to your water feature. You just need to make sure the falls don't freeze over and begin spilling water outside the pond. (If that were to happen, you'd want to shut down the waterfall and place an aerator in the water to keep it oxygenated for your fish.) It is possible that the waterfall alone will create enough agitation in the water to keep some of it from freezing. It will also serve to oxygenate your pond, but if you have a heavy fish load, you may want to supplement with additional aeration to ensure the fish are getting plenty of oxygen.
Both a heater (de-icer) and an aerator are capable of maintaining a hole in the ice, knowing which is most appropriate for you depends on the specifics of your pond. If the temperature in your area never drops below 20°F, you may be okay with just running the waterfall like you do the rest of the year. If you're on the threshold of that limit, you should supplement with an aerator. When using an in-pond aerator during the winter, place the air stone on the shallowest shelf of your pond to prevent the icy air from super-cooling the bottom of the pond. If your winters do have sustained air temperatures colder than 20°F, aeration alone may not be enough to prevent the whole surface from freezing and you'll need to use a floating heater (de-icer) to maintain a hole in the ice.
Heaters and aerators aren't mutually exclusive, you can certainly run both at the same time. For the maximum efficiency, place the air stone directly beneath the heater
It is a good idea to keep a record as you monitor your pond's water temperature during the fall months. This will help you learn to recognize when it is time to perform seasonal maintenance. As the water drops below 70°F, it will soon be time to switch to a cold-water food for your fish. The right cold-water food will have less protein, more fiber, and probiotics to help your fish adjust to a slower metabolism. Begin giving them this cold-water food when the water drops to 65°, and keep an eye on the thermometer. You should stop feeding your fish altogether when the water drops to 50° and below. They will not require food again until the spring.
Now that you know what to do for your fish in the winter, you can rest comfortably with the confidence you are taking the right actions for your fish and their health.