I realize with these last two posts I have created some confusion. Let me try and explain:
When our posts are written, one is written for farm ponds, which pertain to a much bigger pond than your average decorative koi pond, and also much deeper. Ponds ¼ acre or above with at least 5 or 6 feet of depth are what we consider farm ponds, while a decorative water garden, we tend to think in gallons instead of acres. An example of our classification would be a 3,000 gallon watergarden as opposed to a ½ acre farm pond. Also, farm ponds are almost always earth-bottomed whereas watergardens are almost always lined. Of course, every rule has its exception, but these classifications are the clearest way to categorize the two types of ponds.
During the winter, koi in decorative water gardens, as well as bass, bluegill, perch, and other game fish in farm ponds will travel to the warmest place in the pond, usually the bottom. In farm ponds, the water will stratify in the reverse of the summer keeping a warmer layer for fish to live in on the bottom of the pond. When temperatures dip well below freezing (down to 0 degrees F), farm pond aerators can circulate too much of the cold top water to the warm layer below and stress out fish, possibly leading to death. This is why it is a good idea to keep farm pond diffuser plates just a little shallower than the deepest point, leaving a refuge from these rare extreme cold events. Again, these events occur in the much Northern climates and also is rare.
Watergardens are typically not large enough to stratify, and will track ambient temperatures down to the 32 degree mark. Watergarden fish in this situation are gradually introduced to the cooler temperatures and do not stress as much in prolonged cold situations. A properly sized water garden aerator is very beneficial to run all winter long, as it will keep oxygen levels up and toxic gasses out.
In either case, super-cooling of water to the point where fish are lost is relatively rare. It is much more likely that fish would suffocate from lack of oxygen or toxic gas build-up underneath the ice because of the shut-down aerators than to die from super-cooled water. The benefits of running either a farm pond or watergarden aerator greatly outweigh the slight risk of super cooling.