MCA: depends on depth of pond, amount of water movement between floor and surface. In our 8" pond there is no difference as the air domes and TPRs and shower returns keep all the water mixing. If you have stratification of water....not enough current for koi.
MCA: very likely. But the best way to keep in the heat is to cover the pond surface to keep off "wind chill".
MCA: Definitely not true. If it were when I ran our two showers in 20F air temps the showers would have been big blocks of ice. They were not.
MCA: No. The air pumps cool themselves via the pumped air. So the pumped air is slight warmer than surround air. So take advantage of that warmer air by putting a clear pool cover (like heavy duty bubble wrap) over the pond...or floating on the surface of the pond. If it floats on the surface, you like need to bypass waterfalls/weirs that feed the pond.
MCA: and how will skimmers help remove any organic material (fish poop) in the pond floor? Run you pond as in summer. Just put a cover over the surface to reduce wind chill. Bypass any waterfall/weir as needed. Also you can turn off showers if you already have enough filtraiton...and the chilling effect is too great. And last but not least, consider active heating by gas, electric, or solar devices.