Derek Broughton wrote:

I have heard that your fish and sunken plants still need sunlight. As
long as you do not completely cover the surface of the pond ...

They get perilously little sunlight in an ice- and snow-covered Ontario
pond, whether it's covered or not, so I'd say no.

But an ice covered pond is cold. This pond is going to be covered and
insulated and heated. If you have heat, you need light. Heat promotes
activity. Living things need a balance. Any heat should only be
applied when the water temp is threatening to freeze over the top of the
pond. Otherwise it should be off.

An air pump would do this job much easier than a heater and a water pump.

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