We're in Colorado so believe me, we know about freezing
Most pond forums will say 18 inches or deeper and keep water moving.
Our pond is 3 feet deep at on end and 18 inches at the other. We have a 3 section pond, large end then a stream to a smaller pond. We keep the pumps going through the winter and also use a stock tank heater in the big end and a floating ice melter.
here's some pictures to give you an idea of what I mean about the shape.