Waterfalls with submerged pumps are likely to do better than external pumps during cold winters. If you don't plan on running your waterfall yearround, then the best option is to remove your pump and store it in a bucket of water in a location that does not freeze. Storing your pump in water will prevent the rubber seals from drying or cracking. If your area experiences mild winters, you can leave your waterfall running throughout the season. Keep an eye out for ice forming around your pond or stream however, as this can divert the flow of water and cause flooding outside of your liner.
Evaporation still occurs even in the cold winter! Keep an eye out on water levels and add extra water when needed. A pump running without enough water can be a serious hazard to the pump itself.