Can I store hosta in their pots in an outside enclosed, non-heated shed over the winter? Should I cut them back before they start shriveling up for the winter?
If you're keeping them in pots, they need to be in a place where they won't go below freezing, because plants in pots don't have the insulation of the ground to protect the roots. Don't cut the leaves back until they've shriveled - the rhizomes use the materials in the leaves to store up food for the next year's blooming. Hostas in your area should be perfectly adapted to overwintering in the ground (they're hardy to zone 3, even 2 some people say) if you want to use them that way. These articles might be useful: https://www.gardeningknowhow.com/ornamental/foliage/hosta/growing-hosta-plants.htm