When local gardeners speak of a hardy begonia, they almost always mean Begonia grandis (the plant long known as B. evansiana). Claims of hardiness are sometimes made for other species, but to my knowledge none of these has proved to be enduringly hardy in our climate.
The one shown above, Begonia sutherlandii, is sometimes cited as a hardy species. In fact, my start with this species came from plants brought to our local rock garden group's plant exchange years ago. The donor claimed that they had grown in his garden for years with no special protection. I tried it here in the open garden and never saw it after the first year. It will survive in the rain shadow of the eves right against the house wall, and although I have not tried it there, I'm sure it would do well in a cold frame.
At the end of the growing season, before the plants die down for the year, numerous little vegetative propagules appear in the axils of the leaves. It's a simple matter to collect these and store them dry in a zip lock bag in the refrigerator (cold is probably not necessary) for the next year. The main plant will survive from year to year from a compact, tuberous, underground, perennial stem; if the plant is growing in a pot, simply store the pot somewhere dry and above freezing.
The little flowers look like those of a bedding begonia of the semperflorens sort, and the orange color is unusual among commonly cultivated begonias. This is a small (rarely as much as a foot tall in my experience) and rather dainty plant, so keep an eye on it.