In your list of tropical floaters you state frogbit. Frogbit is not native in America but here in Britain it is native. Britain is not a tropical country! However, frogbit is normally annual. Please correct this. Other non tropical floaters include water soldier and water chesnut.

I think there are more than one species of frogbit. I have frogbit in my 50 gallon aquarium. I've put it into my pond. It does not overwinter and survive where I live (Zone 6/7 in USA). Water soldier and water chestnut are not regular sorts of floaters in that the roots are usually anchored in dirt, etc. while the leaves float. In that sense, they are kind of more like mini water lilies.

Frogbit does not overwinter in the UK either. It is an annual but is native.