If you do use a bubbler, be sure it is run in the top one-third of the pond's depth to prevent undue chilling of the depths. Pond cleanliness is critical. Organic sediments decompose with anaerobic bacterial action and produce fish-toxic hydrogen sulfide. Sedimentary accumulations harbor pathogens and parasites that can attack and harm your fish when their immune systems are essentially dormant. A hole left open in the ice ensures the escape of these toxic gases.
Fish are generally safe under a completely frozen pond for up to a week.
This allows plenty of time to properly melt through a hole, if necessary. Avoid fish-dangerous sound wave concussions from breaking the ice. While pond literature suggests melting a hole with a hot tea kettle, in practice, this method may be all but impracticable. Better to set up a floating de-icer to melt its way through the ice layer. Even better is to be prepared in advance.