Winterizing

I live in Northeast Ohio and just purchased a houe this summer with a
small pond. It's about 120 gallons, and was a mess when I first saw it.
It had nothing done to if for 2 years and was full of sludge and no
real "life". I nursed it back to health and it is stocked with a couple
of goldfish, two small Koi, lots of water lettuce, small floating
plants, some "grass", and I plant that I think is a Canna.

My aquatic experince is limited to mostly sal****er / reef tanks, and
no experience in ponds, especailly in winter in Ohio!

I'm preparing the pond for winter. The filters have been cleaned
(external basic wet to dry setup). I plan taking the UV sterilizer off
for the season. The leaves / acorns all almost gone and the pond is
netted. I purchased a floating heater to maintian an area for CO2 / O2
exchange and plan on running the filter during the winter (output will
be channeld back into the pond via tubing).

Questions:
Is it OK to run the filter during the freeze?
Should I "cut back" the plants (right now they are very high and the
netting is just covering them)?
Should I revome the floating plants, or will they survive and regrow in
the spring?

Anything else i should be thinking about?

I plan on doing a major upscaling of the pond in the sping, but I
really don't want to lose anything that I have int here now.

Any help would be appreciated.

Thanks