This is an old question, but people needs to understand how this is done properly.
You need to keep an open, ice-free area in your pond but this does not need to be large. One way to do this is to use an aquarium heater and a sheet of styrofoam, you simply make a small hole in the styrofoam and put the heater here. (Note: the styrofoam is to keep the heater floating in the surface of your pond).
If you want to keep the pump and filter running during the winter, you need to move the pump away from the deepest part of the pond. This is to keep the water at the bottom of the pond undisturbed - in other words, this is to avoid your fish having to swim and use energy constantly during the winter as they do not eat at this time of year.
Some information about overwintering pond fish could be found in this article (source: plantsgalore.com).
Before the winter starts, you will need to clean your pond and filter. This is to remove the plant matter and waste from your pond because when waste decomposes, it produces toxic gases.
The temparature in the water needs to be above 2 °C for your fish to survive, but this is normaly not a problem if the pond is deeper than 1-2 meters. But if you live in an area where it is very cold, the pond needs to be deeper.
And last, the oxygen content in cold water is higher than it is in water of a temperature of 20 °C, so in winter the only concern is to get rid of the CO2 (this is why you need to keep an ice-free area in your pond). It is the concentration of CO2 that is dangerous to fish and if the concentration of CO2 is low, the fish need less oxygen. On the other hand, if CO2 concentration is too high it will block the fish' oxygen uptake by binding to the red blood cells). A helpful article about importance of dissolved oxygen in the water could be found here (source: fondriest.com).