What is critical in keeping koi in the winter is the need to maintain some "open water" to allow for gas exchange.
I have used a "donut" heater that leaves a small gap open when the pond freezes over. This has worked fine for me over the last ~10 years or so, but this winter I lost quite a number of koi even though it wasn't that cold a winter.
I am still not 100% sure of root cause, but I suspect that as the fish got larger (oldest was probably 5 yrs old) they consumed more 02 and/or with the warmer periods this winter, gas exchange couldn't keep up with detritus decomposing during warm periods. This winter I plan to add two "aerators" about a foot off the bottom and they bubble and supposedly keep ice from forming. Time will tell, but my battery chainsaw will always be ready to open some ice.
If anyone has any other ideas, I am happy to listen. I have run pumps through the winter and that works fine except if the GFI trips, the pipes freeze and when running, it leaves enough open area that a mink got in one year and cleaned the pond out.
... and of course, through all of this, the three cent feeder goldfish (lottery winners in the goldfish world) are still doing fine.