Theoretically possible, but the risks are high, and it is not recommended. Success would require meeting the following strict conditions:
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Water depth ≥ 2 meters, with liquid water maintained beneath the ice.
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Continuous aeration, using vent holes or an air pump to prevent oxygen depletion.
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Stable water quality; clean the pond before freezing to avoid toxic gas buildup from organic decomposition.
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Healthy fish; only strong adult koi should be considered—juveniles or sick fish face extremely high risks.
Main Risks:
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Extreme cold can cause frostbite or death.
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Aeration equipment failure may lead to hypoxia.
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Once frozen over, it is impossible to observe the fish or provide timely treatment.
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Predators such as waterbirds may attack the fish.
If you must attempt it, ensure:
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Stop feeding in advance and increase water depth.
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Prepare a dual‑power (AC/DC) air pump and a backup generator.
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Regularly check vent holes to prevent them from freezing shut.

Safer Alternatives:
Move koi to an indoor pond (maintain water temperature at 5–8°C) or set up a simple insulated shelter to avoid the risks of freezing.
In One Sentence:
Overwintering in a frozen earthen pond is like a "gamble with nature"—poor controllability and many unexpected hazards. For the safety of your koi, choose a more reliable wintering method.