Jacque, if your water hyacinth grows all year long, then the only way to thin it out is to find someone that wants your excess or toss the extras. They will continue to multiply, so you have to thin then out Very nice WH, BTW! If your lilies don't freeze, it's possible they grow year round, or just slow down in the winter. Those of us who have ponds that freeze in the winter, cut them back, as they will die back anyhow, and that way the stems and leaves don't clog up a skimmer or make a mess on the bottom of the pond. The only time lilies have to be sunk is if they are on a shallow shelf. My lilies are all 18" deep or deeper, so they stay where they are. Ice never gets more than 4" deep here ... so far anyhow.
As far as cattails that someone asked about, you can let them die, and then cut them back, or you can cut them back now. I have cattails, they are still green, although some of them are turning brown. When they go brown, I cut them back to the water level. Doesn't matter if you cut them back below or above water, they will come back from their roots next year. Make it look how you want it to look.
Irises and grasses can be left alone. Again, if/when they die, as Addy said, then cut back the dead stuff. Many of these plants stay green for a very long time.
Try not to overthink plants. If your plants are tropical and you are not in a tropical zone, then you have 2 choices: bring in the tropicals, or toss them and buy new next year.
Addy, while cleaning up things around my pond, I found 3 small pots I had put the star grass in you sent to me earlier this year! Wondering if I should leave it in the bog (in the small pots or bare root plant it?) or bring them in this winter and see if they take off better next year? The only other things that come in are the elephant ears and taros, as they are not winter hardy in my zone 6a.
Today I tossed a HUGE amount of Penny Wart, it had grown en masse in my koi bog. It has taken over my goldfish pond bog, too, but that's ok, that bog is full of that kind of plant. I, too, do nothing to it when winter comes. Just let it die, and if there is a lot of dead matter, gather that up later. It's far less to gather than trying to cut all the stems off.
Lizard tail that I have is planted bare root in my bogs, like Addy says it doesn't matter much on the depth. When it dies back, I gather any dead matter, otherwise don't do anything. It comes back from the roots.