Here in zone 8, put in triple curled parsley plants last year. I had always considered them to be cool-season annuals, but they grow surprisingly well here. Kept some going through the winter (they even seem to be tolerant of mild frost), and planted more this spring. The difference between the old and new plants is noticeable, though. Old ones are deeper green but with somewhat more flattened leaves. Taste is the same, as far as I can tell.
Is there any disadvantage to keeping such plants going through the winter? That is, does the quality of the leaf continue to change?