Correction: Just figured out that they are Rieger Begonias. Same question though. Thanks.

Hi Julie,
I'm not sure if the Riegers need a winter rest period, but I don't think they'd survive winter in an outdoor garden in zone 9. (I lived in the Bay Area for many years.) I hope you get someone with more specific information responding.
... ah-HA, here's a listing in an old copy of the Western Garden book... describes them as houseplants..."Flowers ...appear over a long season that includes winter...give plenty of light in winter. In summer, keep out of hot noonday sun. Water thoroughly when top inch of soil is dry. Don't sprinkle leaves. If powdery mildew appears, control with benomyl. [personally, I'd try neem first.] Plant may get rangy, an indication of approaching dormancy. In this case, cut stems to 4-in. stubs. [book does not say how long dormancy lasts or if it's total dormancy]
Hope this helps...
-perL