Just to add my experience;
we have a natural pond at the end of our road, approx 150K sq. ft, deepest point about 7' and two years ago, during a long winter when our typical January thaw didn't happen, we had a huge amount (I'd have to guess in the low hundreds) of dead fish in the spring. This pond is spring fed and has no river running through it, so it's much like our ponds. In the 24 years I've been here, I've seen this happen twice, with this last time the worst. And there were all sizes of fish, some 12" long. Not a lot of young/small ones, though. It was nasty; even had vultures camping out for snacks.
So, a good amount of rotting vegetation to be sure, fish load = unsure as it's natural, but I have no doubt this kill was from the gas unable to release for such a long time (Winter here is about mid Dec to late Feb).
And just because of that, I'd see about at least opening a hole once in a while. Last year, I chose the aeration model and because our winter was the warmest I've seen in all my life, my pond came close to freezing over only once, and that took the form of slush near the aerator. I'm a little worried if my air pump is going to be substantial enough this winter though, as I don't expect a warm winter again. So, I'll be reading here on the forum for further ideas. And now, off to read addy's links.
Michael