The paper whites will not bloom again, so they need to be tossed. The hyacinths should just be kept in the pots, don't cut the green. When the soil is workable in the spring, you can plant them outside in the garden. It is what i do, and they will rebloom , usually after a few years. I had hyacinths that I planted out this past spring, after forcing them in water, and they bloomed late fall, it was crazy, it will take a few seasons for them to get back in sync.
Cindy

I plant mine immediately in the garden after they finish flowering because we don't have frozen ground. I find they bloom the next spring. There is no delay and they are not out of season so it must be something to do with different climates. However, the blooms are never as dense as the original indoor ones. They will come up every year thereafter.

The paperwhites might bloom again if you lived in a frost free place where they grow outdoors in the normal course of things.

All the hyacinths in this picture started life indoors in water.

Thanks for your replies!

As for they hyacinth I think that means I should put them in a pot with soil,
Should they be inside the house in a cool spot or a sunny location?
Should they be watered very much?
If I think of them as if they were underground in the winter right now - is that what I should try to create for them?

Great photo floral_uk

I guess we shall see what happens with these.
It's been so very cold here the inside of the house can chill bulbs just fine this year.

I can put mine straight outside but it sounds as if yours need temporarily to go into a pot in a cool place first. Then put them out when the weather improves.

Thanks for the help!