Answer: Rex begonias would not be expected to survive a frost, even with covering. If you want to save them from year to year they can be brought indoors as houseplants. The perennial begonia is Begonia grandis, the rest would be grown as annuals. I am so sorry you lost yours.
Greenleaf is a wholesale-only grower. Unfortunately I have no way to check on local retail sources for your, however Rex begonias are available by mail order if you have no luck in your local stores.
Logee's, for example, offers a selection. (You may need to cut and paste the complete url into your browser to make it work correctly.)
Here is more information about growing different kinds of begonias in the home garden
Here is information specifically about the Rex begonias and how to grow them, from the American Begonia Society. These are really popular as collectible plants.
I hope you find some begonias.
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