If you could move the koi inside for winter, and the entire winter. Say a doboy pool inside the garage, or a stock tank(s).
Then in winter, you could install a bottom drain.
Doing this would keep your koi safe from harm. Their immune systems are less active during this time, thus increasing the chance in which your koi can get an ailment, this is eliminated if they are kept warm in a garage or basement.
I suggest you install another skimmer to battle those falling leaves into your pond, but this is optional, but is also good.
I believe you said your filter system was a biological filter, if it is, What kind?
I also suggest you install a Ultraviolet Sterlizer, but if you like the green tinge, then you dont have to, but know this, sterilisers also kill unwanted bacteria.
Beautiful pond by the way. I like the Island, and the natural look.