Rita, I was responding to Arlene, who is in zone 8. But, that's just because I have no experience growing in colder zones... it turns out that parsnips are one of the most cold-tolerant food plants out there. If your ground freezes hard, I'd probably mulch them, at least to make digging easier if you decide to harvest one, but I bet you could grow them over winter even in zone 6. Germinating them was the hardest part for me - we often have warm weather late into the fall, and the seeds prefer cool to sprout. They're best to harvest after a few frosts, so I aimed for February with mine, as that's the only month we reliably get freezing weather - some years, the first frost hit in January.
(I just tried looking this up on Google, and found conflicting results, from "stands a zone 2 winter" to "doesn't take a hard frost". I know the latter isn't true from experience, and have a hard time believing the former... reality must be somewhere in the middle.)
