That's tall! I'm not familiar with a begonia that gets that tall, the largest I've grown is the Dragon Wing, which probably maxes out at half the height you're seeing. But to narrow it down, does it look anything like this?
This is not the best example, but it gives an idea to narrow down the choices.
I was thinking in your climate a tuberous begonia might have a chance of surviving mild and brief freezes in the ground, but any others would at least be damaged if not killed in more severe or prolonged freezes.
You could try asking on the "Annuals" or "Containers" forums as there may be people there more familiar with other types of begonia.
