saving celery seed in winter climates

[Jean in Mt]

Hi All,
Happily I have been able to grow some tasty celery this year. I put a few plants in the grrenhouse and are still growing great. The greenhouse will be given over to frost/freezing by December to kill any buggies. I am wondering about saving some of this celery for seed next year, or even just to have the flowers for insects to enjoy.
How do you think it would work to cut back the stalks and dig up the plants. Then I can put them in the house, warm, or crawl space, about 45 degrees, and bring them out in the Spring. The outside world isn't very plant habitable until mid May.
Thanks for any ideas,
Jean in Mt
zone 3-4