overwintering pond grasses - sink 'em?

I have taken to sinking most of my pond plants for the winter but am
unsure if that is best for the grasses.

My pond is 40 inches deep and I keep a bubbler in it to maintain a
hole in the ice. We are in zone 5B in Southern New Hampshire.

I sunk the Creeping Jenny yesterday but not the grasses. Last year I
brought the grasses inside put them in plastic bags in a cool corner
of the basement and they all croaked.

Advice?

TIA

John