Jim, my experience with winter aeration is that it is not necessary to run it all the time. There is a substantial reservoir of O2 in the pond water going into winter.
I believe our experts will say that if a pond is ice covered for more than a month at a time, some open water from running an aerator is beneficial. And, especially if you are removing snow cover for skating, sunlight will reach vegetation prompting photosynthesis. I'll shut off my air pump for periods during winter.Some winters I've waited for a few weeks after the pond has frozen to fire up the aeration. As my air hose enters the pond water from an above ground location, I have to watch that I don't have an ice plug in the hose at the water level. By turning on the pump on a warmer afternoon, I haven't experienced a problem.
Something I find fascinating to watch is the air plume growing under the unbroken surface of the pond ice and how it seeks an escape until a hole finally opens above the diffuser.
YMMV
