One key factor is to keep the surface snow free so that sunlight can get through the ice.

My non-scientific comment is that the light helps plant matter create oxygen under the water.

I'm not sure, but I don't think winter kill from ice-over is a foregone conclusion.

Excerpt from Robert Crais' "The Monkey's Raincoat:"
"She took another microscopic bite of her sandwich, then pushed it away. Maybe she absorbed nutrients from her surroundings."