Again, air temps don't matter. The only thing you need to think about it water temp. If your water temp is above 50, you can feed them twice a day with a fall food. At 62 degrees, I bet they are still quite hungry, so go ahead and feed them 2x per day.
What can you tell us about your water parameters? Are they not stable? Do you continually need to make adjustments? If so, that is usually a sign that something is off. But when you shut a pond down for winter, you don't worry anymore about water parameters...
When you turn off your pond for winter, you can leave a air stone in, but make sure it hangs in the upper 1/4 or 1/3 of your pond depth so that it does not disturb the warmer water where the fish will hang out/hibernate at the bottom. You do not need to leave your waterfall on, but you can. You don't need to do both, you can just do one of these. If your water freezes in any way, it is best not to keep the waterfall on, because if your waterfall starts to freeze over, it can cause flooding/leaking in other areas as the water slowly freezes in funny angles.
With lilies, you just cut the leaves/stems off and plunge the ugly looking tuber thingee deep into the pond and it will do fine and come back next year (if they are hardy lilies and not tropical). Umbrellas need to be brought in to overwinter in your house as they are tropicals. Simply keep them in water the same way with similar light as they get outside and they will be fine. You need to change the water every few days so it doesn't get stale. You can bring a few water lettuce inside too. Just keep 'em in a bucket with an air stone going and change the water every few days, too. When they go back in the pond they will start multiplying like crazy again.
I'm guessing your koi are probably very small right now in your 300+ gallon pond. But, yes, you have way too many. In fact, you really shouldn't have koi at all. These fish go very quickly, and will soon not fit in your pond. You would be better off with goldfish like comets, shubunkin, etc.
Hope that helps you. Keep the questions coming and search the site, as we already have lots of info like this out there.