Coinr:
I'm in Mi too, so should understand your situation, though mine is a bit different (my pond is covered and there is no external debris, with all plant material either trimmed away or taken out as I shut down the pond). I don't have a skimmer, so can't tell you if it will handle the weather or not, but were it me, I'd take it out for the season, just in case. (unless it's a bear to unhook/take off) I've already unplugged the pump (submersible) and it will stay beneath the ice line for the winter. They say to keep the pump under water(like in a bucket/container), even if you take it out and store it inside. I have an aerator, about 12" down on a shelf, and that's the main means of keeping a hole open for gases to escape. Unless you have a large fish load, oxygen shouldn't be an issue as the cold water (winter) holds more than the warm (summer) and fishes' usage drops as they pretty much go dormant (not the right term, but it escapes me in the moment). I did, however, order a heating element, just in case this winter is more normal (as opposed to our 'near winter' of last year) and the temps remain low without a January thaw. If you don't have a lot of debris that can compose over the winter, and your fish load is lite while your gallonage is high, you should be fine. Last year, I only had 17 goldies but they were busy and now, I have near 100, though most are less than 2" still. You don't have to worry much about the ice covering over unless it's for a long length of time with no break. I plan on keeping the heater unplugged, even if the aerator ices over, unless the ice cover lasts more than 3 weeks. Then I'll plug it in periodically and recreate a hole so any gas buildup can escape. But from everything I've heard/read, you don't need a hole open all the time. At least, that's how I'm approaching this wintering problem.
Oh, re your filter media; since most of the bacteria is also not going to be working for you at the lower temps, I'd take that out and give it a good cleaning, ready for next spring. The waterfall should be turned off, if stories of icing up and ponds then being drained severely are any indication. Still, some keep everything on and working the whole winter. I just don't see the point; there's a natural pond at the end of my road and I guarantee you there's plenty of decomposing vegetation, no running pump/water, and no aerator to keep the ice open. And unless we have NO thaw (which happened a couple of years ago, if you remember), the fish don't wash up on shore. I'm just not taking the chance that the thaws will be on time, hence keeping the ice open as much as I can within reason.
YMMV
hope this helps.
Michael