I did not find the a good description of how to handle forced bulbs once done blooming. I live in MN and was looking for information on how to care for forced bulbs until I can plant outside.
The article has good information but there is a gap in the How To area.
Do I keep them in soil? Let them dry out? Re chill/freeze/ keep room temp? It is mentioned that to chill in a garage, in MN that would freeze them. Lot more detail is needed.
The most stressful thing a flower goes through is blooming. Most of a bulb's energy is spent after flowering. For the plant to survive and possibly bloom next year, the leaves need to be under supplemental lighting (northern winter sun is a poor substitute)and kept watered and lightly fertilized until they turn yellow. At this point, bulbs can be removed from the soil and kept in a paper bag in the refrigerator. In early spring, plant them 3 x the depth of the bulb. e.g. A 2 inch long bulb is planted so the tip is 6 inches below the surface. The plant may send up leaves but re-blooming this year is less likely. Some bulbs transition to the garden better than others. Paperwhites are not hardy in the US except the coastal areas of the South. They should be considered an annual and consigned to the trash or compost after bloom is over. Hyacinths and species tulips are likely to survive and reward you in spring of 2020. Fancy hybrid tulips are often short-lived and do not reliably bloom again. Since you may not know which tulip species you have, plant them out and see what happens.
Freezing, by itself, does not seriously harm a bulb. However, if a bulb in a pot freezes then repeatedly thaws when a break in the cold weather occurs, this can turn the bulb to mush. By the time the ground has frozen to the depth of our in-ground bulbs, sudden temperature swings have less impact. It takes quite a while for the ground to thaw at that depth. If you forced the bulbs in water, I would throw them out. They are utterly spent.
You see that there is no one answer to your question. Saying "it depends" is an unsatisfactory answer but promising results would be misleading. If you like to take chances and experiment, follow the instructions given above. Results are not guaranteed.