If possible, dig up an area (I use an end of my veg garden) and put the plants in the ground in their pots or burlap or bags or containers. Put them in so the roots are below ground level, then water them well and mulch them with leaves, grass clippings or any mulch you have to hand. Put them close together with just a small amount of soil between each plant in the row. You can get lots of them close together. In the spring, pull them out of the ground and take them to their new home.

I nursery hundreds of plants each year this way. I grow lots of perennials from seed and like to get at least a couple of years growth on them before they go into their permanent homes. I also do lots of propagating, and want several years growth on most trees and shrubs before they get planted. I rarely lose much by doing this each year, though some loss is inevitable.

You can split and wrap the hostas and bury them as above. In fact you can use cardboard boxes or anything that will hold the plant over the winter, as long the roots are covered with soil to protect them from winter conditions, of which drying out can be the most insidious.

The garden shed or unheated garage might work, depending on how cold/warm it gets in there, and what zone your plants are rated for. Again you will need to make sure the roots don't completely dry out (or remain too wet). I think I once read something that being out of the ground is the equivalent of 2 growing zones, so if your plant is hardy to zone 5 and you are in zone 7, it can be left in a pot without further protection. In general, in the ground is the best place for a plant. I have several standards in large pots, so I cover the sides of the pots with plastic to protect them, and bung the whole shebang in the ground.

Hope this helps.
Rosalinda

I think the hostas would come back if you just planted a piece of the root. It's a tough plant to kill.

About outside winter storage of potted hostas see threads in the hosta forum. People there place potted hostas on the side to avoid rain pooling up inside the pot and rotting the plant. They stack the pots like a wood pile in the shade of the house or under a conifer and place a plastic cover over them. This will also prevent repeated thawing and freezing which kills plants.

Ctpalmtrees.com/winter-plant-storage