Because of my personal experiences with natural small lakes and large ponds, I disagree with the statement that CO2 and other gases / compounds such as ammonia and H2SO4 cannot reach toxic levels during winter. If the ice over the pond becomes thick and solid (hard ice with no porosity) and there are no openings to the air above, these gases and compounds can accumulate and O2 cannot exchange into the pond either. The source of these gases and compounds are detritus, uneaten fish food and natural fish waste from their excrement as well as their "breathing".
Here is a good article regarding wintering a Koi pond:
http://www.pondtrademag.com/articles/ar-73/
However, the author mentions one thing that I am certainly not in total agreement with. He does not recommend removing snow from the pond ice. Although shoveling snow off a pond surface may prove unwise for the obvious safety reasons, there is a major drawback to having a total (and thick) snow cover over the ice. If it is sufficient to block all sunlight, then any beneficial bacteria and plant cells which cope at these lower temperatures will not be able to produce O2 via photosynthesis and will not be able to break down any harmful compounds including ammonia and nitrogen. Yes, even at 32 degrees, some of these bacteria and plants are still alive and functioning. Some areas of snow cover over the ice would help to insulate the pond to maintain its temperature, but you wouldn't want the entire surface smothered in deep snow.
Here in Nebraska, a small lake or pond that is protected from the wind during winter will experience a large winter kill because the wind cannot blow the snow off the ice to allow even marginal sunlight to seep through. During the year that the author mentioned (2009) we too experienced that cold here in Nebraska, with lots of snow as well. One of the nearby lakes where I fish often is an oxbow lake and it is nestled in a dense grove of trees and sunken down below the landscape so that the wind cannot reach the surface to blow the snow away. When spring came and the lake thawed out, there were thousands of dead fish littering the lake.
With all the trees surrounding this lake, it was full of detritus (leaves and sticks). With no openings in the ice, none of the gases from the decay of this material nor the ammonia from the fish could escape and no O2 could be absorbed from the atmosphere nor produced by any vegetation.
There was another winter when this occurred for a lake which was about 8 or 10 acres in size. This lake contained a lot of huge spoonbill cats. It was a very sad sight to see all these fish and other species dead.
Catfishnut