Sorry to hear of your dead fish.
I have had my fish outside for over twenty three years and have no trouble in the minus 40 below here in Canada. I would never trust or use a air stone or bubbler. My pond set up is different than most, and I do everything pretty much different than most.
I have only very big pre- pump filters that are all under water, this way they tend not to freeze.
I never shut down the main flow, that keeps all three connecting ponds circulating. The main pumps runs and the extra summer pumps are put away, like spitter, and no big splashing waterfall, just water ways that keep the three ponds circulating as one pond.
The running water all winter keeps the top ponds from freezing as hard, although I still can get lots of ice, despite the use of a big heater floating where the water moves well.
I check my ponds every day in the extreme cold, some times several times a day during the most extreme temperatures of minus 40 below. Then If that is not enough, I also peek out the window in the bathroom several times a day during the coldest weather too. I also top the bottom pond every day when extremely cold, to make sure it will have lots of water to keep the system flowing, as water gets displaced and turned into ice on the top ponds. I have spare hose in house and run it out the window to top up ponds during the coldest months.
Large koi need clean running water all winter, so why does everybody put the filters away in the winter? Ice cold water does not always equate to crystal clean clear water, that is why I leave my underwater pumps and filters run all winter. Get a good pre pump underwater filter to keep the water fresh, that will be big enough to run all winter without clogging up. and enough of a current to keep with water fresh. Ice also melts away much quicker if the water is running all winter, and ice will not get as thick either.
Last but not least, get a good floating heater, I have a 1250 Watt that I used most of this year, and I switch to the 1500 watt floating cattle heater when below minus 30 or so degrees. Place the heater where the water moves well, so the water is evenly heated.
Keep a watchfull eye out all winter, ensure that the pond is moving and that there is lots of water below the ice.
That is my best advice and good luck in the future. I am sure you will figure out a way that will work good for you as you gain more experience too.