Catfishnut, you are absolutely correct as concerns large earthen ponds. However, the average Garden Pond normally goes through a 'closing down' process where most of the organic debris is removed before ice-over. This is not done in a earthen pond. In fact, in an earthen pond this organic debris accumulates over years before any action is usually taken (dredging) to remove it. Natural earthen ponds have been known to experience toxic gas based events in warmer months of the year also.
I couldn't agree with you more about the importance of snow removal Sunlight is all important in maintaining an algae growth that contributes Oxygen to the water column.