I wouldn't give up on it yet. Durantas seem to be able to come good after dying back from dryness/heat. My guess is they'd be able to come back from a "cold pruning" as well.

Is this a perennial?

I only have Duranta "Geisha Girl", it's a blue colour. They are a perennial shrub and normally grow throughout the year. One of mine was planted where it got no irrigation and had a lot of die back during the dry. But it recovered quite well when I gave it water and rain came.

Cold penetrates leaves quickly, it takes a lot longer to penetrate the stems and branches. So exposure to cold for only a short time would likely only cause damage to leaves and the thinnest branches.