Pond filters are not needed throughout the winter months, but ponds containing fish must have their dissolved oxygen levels maintained to prevent fish death. The danger with running a pond filter and pump in winter lies in intense temperatures doing damage to your pump or hoses. Keep some mitigating factors in mind.
If your pond has fish, supplement your pond's oxygen levels through an air stone or air pump, if you are intending to turn off your filter and pump for the winter. A few air stones can be placed at various spots in the pond to provide oxygen for the fish, should the surface water freeze over. Fish can survive for some time in a frozen pond, but the chance of injury or death is decreased by using a pond heater to keep a hole melted in the ice. In a pinch, a pot of boiling water placed on the ice can do the trick as well.
If your pond or water garden only has aquatic plants and no fish, you can safely turn off your filter after the last of the vegetation has died off. This usually occurs in mid-January. Use a skimmer to remove excess floating debrisa,then shut off your filter for the winter. In spring, you may want to do a full water change, as a frozen pond is as much a magnet for leaves and debris as it is in summer.
If your pond filter is running purely to prevent an algae bloom, you can shut off your pump considerably earlier. Once the first frost hits, usually around late November, the chances of having an algae bloom decrease considerably. Shut your pond filter down after temperatures consistently drop into the 30s Fahrenheit in the evenings, and your pond will remain algae-free for the rest of the season.
Some pond owners run their pumps and filters purely to keep the water from stagnating and mosquitoes from taking the opportunity to lay eggs and hatch larvae in the water. In the heat of the summer, in as little as a 12-hour period, mosquitoes can lay eggs and larvae will begin to hatch in a still pond. If you are keeping your filters and pumps running purely to keep the water moving for pest control, you can safely turn your pumps and filters off in late October and early November. As temperatures begin to fall, mosquitoes become less of an issue, and your pond will be peaceful and bug-free.