In winter, is pond water warmer with or without a fountain? I have goldfish
In nature, fish survive in ponds due to a lack of turnabout of water.

(Fresh) Water has its highest density at 4°C, meaning both warmer and colder water float on top of 4°C water. Wind may push surface water to the bottom, slightly lowering the temperature at the bottom of the pond. Still, once the surface starts to freeze, this proccess is discontinued, creating a temperature-gradient with the relatively warm 4°C water at the bottom - until spring. Thus fish don't freeze to death.

Meaning, leaving your fountain running is a rather bad idea.

As to the issue of possible lack of  oxygen - I can't answer that reliably.