"I live way way north of you. Here's some plants I've seen in the river out
back:
Elodea.
Ludwigia (I think)
Riccia.
Sag (or val)
(more than I forget offhand)"
Elodea, Ludwigia, and Sag include cold water species that are native to
North America. I doubt that they would appear on any invasive plant list,
but if they ever did it would further illustrate my point.
I don't know about the Riccia. But if it is really that plant,
it is most unlikely that it could survive in a cold, dark northern winter,
let alone grow to nuisance proportions.