Those of us that live in colder climates with freezing winters hate for our koi to suffer from bitter cold temperatures. JR can scare you with his tales of how fish that 'live under the ice' in northern zones can have their health drastically compromised as they recover from winter in the spring.
I built our 2 ponds 5 years ago. For the first 3 winters the ponds would freeze over. It was all I could do to keep a hole open in the ice. Three winters of this made me want to try to get a cover over the pond and devise a way to keep the water temperatures up in at least the mid 40's for the winter.
Here is a picture of our koi pond from one of those early winters. The ice is about 3" to 4" thick. Water temperature was probably not much above freezing, maybe mid 30's F.