Planting them would by far be the best option. In the shed or under the deck maybe will work if you protect them.
What kills plants in containers over winter is the thaw-freeze cycle. They need consistent temps. one way is to cover them with leaves, pine straw or straw. They can't be exposed to the rains and get too wet. The shed would work, but unheated I would put chicken wire, or hardware cloth around the pot, and fill with straw or the like. To insulate them. So they do not freeze and thaw as much. This may or may not work. I overwinter in an attached garage and the plants do OK. Slightly warmer, consistent temps, no overhead exposure to rain and wind.
Again the ground is best and as long as workable you can do it.
I grow strawberries in ground, yet they need to be covered by straw (thus the name!!). Also I have blackberries not really hardy to my area, but I use leaves to cover and they survive. Temps remain consistent, and no drying wind exposure. Some are upright and I spray them with an anti-desiccant which is like a wax coating that prevents them from drying out. What happens is the roots freeze, the plants dry from the wind, but the roots cannot work being frozen, so the plant dies from dehydration. Often the roots survive, but no fruit the next year! This method really works well for my plants and I have hundreds of blackberries to prove it.

Well, I went ahead and planted the sage next to the shed - we'll see how they do through the winter. Common sage is supposedly hardy to zone 5, so as long as we don't get a winter as nasty as last, they should be fine.

As for the parsley, I have an idea. What if I harvest the leaves, dig up the taproots, and put them in the fridge for the winter? Basically, I'd be treating them like you would tulip bulbs or something.

Parsley is a biennial in my garden, so that even if it survives the winter, its main energy goes into blooming and producing seed the second year rather than producing leaves. Just let the parsley die and start over next year with new plants.

I would agree on the parsley. I never grew it, but picked up seeds for next year. If as stated it is a biannual, nothing you can do to keep it. Although you could harvest seeds from the plant. That actually would be cool. You would keep the cycle of life going.

Yeah, I'd definitely like to harvest some seeds if possible. Unfortunately I made the mistake of pruning back the flower spikes over the summer, and I've heard that parsley may only flower once. Is that true?

I don't know? Maybe ask this question in the herbs forum.
I myself have a lot to learn about herbs. I want to grow a hybrid basil, so it has to be brought in. I have heard that you can take cuttings and start new plants over winter. This may be an option we have not considered for other herbs?

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