Believe it or not, the answer is both "yes" and "no"!
Rooted plants will continue to make oxygen in your pond over the winter. This is even true in upstate NY for ponds under heavy ice cover.
Winter kill generally occurs when you have long periods of snow on top of your ice, due to complete blockage of the sparse sunlight.
Will you be able to aerate your pond? If not, can you sweep the ice if you get a heavy snowfall that does not blow off?
The way rooted plants can possibly make it worse is that when living things die off in a pond, the decay process actually consumes oxygen. If you have a pond with lots of dead leaves and muck on the bottom, that then suffers some vegetation die off, you will almost certainly then suffer a fish kill.
However, I think the rooted plants are almost certainly a huge net plus. I am not an expert and live in warmer climes. Hopefully, one of our experts that lives in the North can chime in with some better information.
