@max384 and rebelangel_3733: I'm located in Northern Colorado, and we get temperatures down to -20 at times. My previous pond was made of two pre-fab plastic liners for a total capacity of maybe 250 gallons. Over the last four years, I have always kept my pump and filter running through the Winter, however there is a caveat with this... If the pump stops running for very long, your pipes can freeze up. Assuming everything continues to run well, pushing the water through your filter will still help with mechanical filtration - removing dead plant matter that is still in the water. Also depending on your setup, the extra agitation can help stir more oxygen into the water, which the fish need a lot of in the Winter.
Adding a bit of heat to smaller ponds is actually pretty easy. Check with the farm supply stores for a stock-tank heater made to go in plastic tanks like the rubbermade types. These will be insulated to keep the heater from melting your pond liner, but you need to be careful of when you use it. I never plugged mine in until it was cold enough outside that the pond was nearly frozen over. If you're not careful, these heaters will have your pond back up to 45 degrees in the middle of Winter, and your fish will be wondering why they aren't getting fed! If you can afford a good heater, some come with an adjustable thermostat, so you can keep the water temperature down around 32-35 degrees.