My Ti plants do that every winter. As long as the roots don't freeze, you'll get new growth.
Next time a freeze heads your way, you can cut them off @ soil level, stick in a bucket of water, roots will appear within a week, then plant back in the garden. Water well to get it established. Eventually you'll have a LOT more from doing that, and never have to start a season with ground-level-only plants. Or if you turn a big trash can over them for the frozen night, you might not have any leaf loss.