I found my Azolla in a wild pond by a bicycle trail. My hubby waded out in his undies to get it for me when no one was looking
You can add that stuff to your pond anytime of the year. It is a really tiny floating plant that spreads over the pond. I have no trouble keeping it contained and I have some in my pond right now that the fish are actually allowing to grow. Now you said you have koi right? Well they may mess w/all the plants you put in your pond. Like I said I have only goldfish and they aren't too bad w/most of the plants. In the Spring/Summer lots here share plants w/each other when they have excess and just ask to be reimbursed for the shipping. My parrots feather is dwindling for some reason this year. I think cuz it didn't like my bubbling huge aerator. I may have to acquire some more next Spring if the 2 pieces I have left don't start spreading.
Most plants I'd wait till Spring to acquire. The reeds and rush plants you can buy at most garden stores and they will grow in a pot in your pond raised up so just their roots are immersed in water.
Hornwort is a neat underwater plant and Colleen in Canada who has koi here has lots of that growing in her pond. The koi eat it but she always has some spare on hand and it grows like crazy in her pond even w/koi.
Just remember what I said up top there. Koi can wreak havoc on plants........some do, some don't. There are ways also that people here who have koi have come up w/ to protect their plants from their koi. Maybe post that as a question on a new thread and peeps will chirp in and make suggestions.