I'm a novice when it comes to begonias, so please pardon my ignorance....

I planted some run-of-the-mill garden center variety begonias in window boxes on the east side of our house last spring, and they did quite well. Now that winter is approaching, it seems a shame to just let the frost kill them, but a couple years ago I tried to bring a couple begonias inside and they promptly dropped leaves and died. [I don't think they like our woodstove] I tried running a humidifier, keeping them in a cooler room ect., but to no avail.

Could I keep them in the basement, and if so, should they be cut back or not?