Yeah, there is the "natural swimming pool"

Koi will do very well in that pond, Shamu - but I would put something in there that keeps at least a small spot from freezing. It might be a de-icer, or it can be something as simple as a pump that simply has its outflow directed to the water surface. Of course, a tiny little pump, like the ones for an aquarium, wouldn't cut it in a lake like that.
That "air" that builds up under the pond and causes the ice to break is exactly the same air you don't want your fish exposed to. You have to have one spot in the pond where the air exchange can take place, and the anerobic air doesn't have a chance to cause any harm. It might not matter too much with the local fish that are in there now, but a koi is definetely something else.