Different plans can calculate some of these things a bit differently, but because of the calorie and carbohydrate count, I would consider it a carbohydrate.
I follow an exchange plan, and carbohydrate choices (fruits and starch exchanges) generally contains between 50 to 80 calories. Vegetable exchanges contain 35 calories or less per serving (usually about 1/2 cup cooked, or 1 cup raw).
1/2 cup of cooked parsnips contain 55 calories, so I would call it a carbohydrate or starch. I double checked in my "Exchanges for All Exchanges" book, and they list 1/2 cup of cooked parsnips as one starch/carbohydrate.
My Etsy shop (currently closed for the summer)
When I was looking at south beach diet, I believe it listed parsnips as one of the foods that was of the foods it listed as having a high GI and not recommended. So really I'd count it as however you'd count a potato.
You can't out-exercise poor eating habits.