Being from a cold prairie climate, overwintering potted hostas can be a real challenge. I decided to conduct an experiment late last fall with two potted hostas that I had not yet planted in the soil, Fire and Ice, and Sum and Substance. Fire and Ice was a plant I had for several years that had kind of languished in its garden position so I dug it up and potted it for the summer; Sum and Substance was a newly purchased plant in 2015. We have a small outbuilding on our property that is somewhat insulated but not heated ; I put S and S in there. F and I was left outside until about early Dec and then was brought indoors to our heated attached garage where I keep my grow light stand. In mid- late winter I noted some growth on Fire and Ice, but nothing ever progressed. I guess it just didn't have enough winter dormancy. Sum and Substance, though, is pipping, so hooray!
I plan to grow a few more potted hostas this year and will try storing them again in the shed; hopefully they will survive!

Fire and Ice struggled here, each year I think it will not return, and again so far it has not. Sum and Substance I have only had a couple of years but it has been very a very robust plant.

Debbie - I have a porch which is entirely enclosed with windows but not heated or insulated. I've had about 50% success with trying to overwinter hostas in pots there. If I really want to keep a hosta over the winter, I bury it in my veggie garden - pot and all unless the pot is is special and at risk of breaking.