Thank you for the comments. I blanched them and now they are in the freezer... let's hope I remember they are there the next time I need parsnips!

I think with parsnips, especially for longer than a few days storage, I'd peel, blanch and freeze. I'd worry if I peeled and refrigerated that they'd turn brown. Don't have any experience with it, but since a lot of light colored veggies have that tendency, I wouldn't risk it. If they already weren't too old, I'd keep them as is, skin on, un-chopped, in the cripser and try to use them within a few days. But longer term, peel, blanch and freeze.

I would peel, cut up and cook them before freezing - just a quick blanching should do. But if you're going to do all that work, can't you just add them into something you're already planning to cook this week? You could sub them for a carrot in a soup recipe, or grate them up to add to a slaw (raw).