If a pond is around 75% ice covered, that ice acts like a blanket, insulating the water from the cold air. Water temps will usually be between 38-42 degrees under ice. When we get cold snaps here, air temps drop into the twenties and teens. Water freezes at 32 degrees, so if you are running a waterfall when temperatures are below freezing, the water temperature can drop to dangerous (for the fish) low temperatures.
Make sense?
Regarding other things that go wrong over the winter - koi and GF are temperate water fish, and not really adapted for the cold. They lack the ability to really stay active (like trout) or hibernate (like frogs), instead they go into torpor, which means they basically hunker down and sulk until conditions are livable. Their immune sytem pretty much shuts down. The good bacteria in the filter are less active during the winter, but that is ok, because as their metabolism slow down, they produce less ammonia. However, solid wastes (and plant or leaf debris) that are left in the pond over fall and winter will feed the 'bad bacteria' that can also attack the fish. It is very important that the pond goes into the winter nice and clean.
We tend to stop testing the water (and doing water changes) once cold weather hits. Since there is less biological activity, we tnd to think there is no reason to worry. However, there is still some biological activity, which consumes the carbonate buffers (KH). Rain and snow also dilute the buffers, so testing the KH over the winter is important. You can bring it up with baking soda (sodium bicarbonate).
Because the immune system doesn't really kick into high gear until water temps are in the mid to upper 60's, and because solids build up over the winter, promoting the bad bugs, spring is when we often SEE problems that have been brewing for months.
I like to do a good clean out during the fall, dome the pond over the winter, and then do a nice big water change from the bottom of the pond in spring. If filters have been shut down, don't drain the mucky water into the pond when you clean them out. Before doing a major spring pond clean out, you should wait until water temps are at least 60 degrees. Netting fish is very stressful, but that is a whole 'nuther topic. (GF tend to be a bit more rugged than koi, but the some concepts are true for both.)
Good luck!
