This is a very common question asked by pond keepers in the UK where temperatures can reach subzero and consistently stay at low single digits for long periods of time. Firstly, with Fish being cold blooded animals their metabolism is affected by temperature so the colder it is the less they will want to feed, with exception to Sturgeon and Sterlets who will continue to feed throughout the winter periods. During the colder periods a reduction in feeding is expected often feeding only once a week and even a complete halt of feeding in the coldest temperatures.
The next thing to think about is filtration systems, although these are vital for the rest of the year to keep the water parameters in check during the colder periods of the year where water can freeze it is worth turning all pumps off. The reason for this is even running water will freeze at 0c so the last thing you want is water to freeze in your pipes and hoses which then results in excessive pressure pushing outwards causing the pipes and hoses to split ultimately leading to leaks when the water is once again running.
The last thing to consider is the oxygen levels for the Fish. If the temperature drops to 0c the water in your pond can freeze, in the deeper parts of the pond especially if dug into the ground the water is unlikely to freeze. However the surface layer will very likely freeze and if it does the vital gas exchange of oxygen entering the pond and Co2 exiting will be affected. An old school fix to this is to leave a couple of tennis balls floating in the pond so when the water does freeze you can pop the balls out leaving behind air holes. You can also break the ice but be careful as large heavy chunks of ice falling in the pond can damage the liner/walls of the pond and not to mention may hit the Fish. These days you can also purchase pond ice vents and pond heaters, these aim to produce a small area of heat that will keep the water in its immediate vicinity to not freeze.
