Hi,
For last winter I just cut all dying lilly pads away, but left any pads that looked healthy. Once winter started nothing seemed to happen to the plants, so I left them alone until spring.
I have 2 water lillys, some elodea crispa, and some water soliders. They all came back very well this year, even after the severe ice last winter. In fact I have had to regularly remove elodea crispa and water soldiers this year, as they have been growing like topsy.
New for this year, I have two hyacinth pickerel that are ~3ft down. They shot up a good three foot above the water line and both plants flowered. I have cut all the leaves back below the surface now as they were starting to turn. I hope they survive the winter!