In Season: Parsnips require cold weather to convert their starches into sugar and develop their appealingly sweet flavor, so they are harvested in the late fall, after the frost sets in. They store well and are available throughout the winter and spring. What to Look For: Parsnips look similar to ivory or pale-yellow carrots, with a bulbous top tapering down to a skinny root. Choose small, firm parsnips that are not limp or shriveled. How to Store: Keep parsnips loosely wrapped in the produce drawer of the refrigerator, and use within two to three weeks.