Central Minnesota, here. Our cedar tree always turns purple-ish in the winter - especially last year’s fresh growth. However, this is just it winterizing itself. It’ll green up again as spring progresses. If yours is anything like ours, I bet it’ll be just fine. As long as it’s not brittle and disintegrating, I don’t think it died.

That said, if it doesn’t green up in the next month, then I’d say you may have an issue.