Get some dirt and moisture on those roots right away, peony roots are tender. Planting them in pots sounds like a good option. Use light well-draining soil, and leave the pots outside all winter long, in a relatively warm spot that isn't too sunny. Water them during warm spells but make sure they don't get water-logged. They should be fine. Good luck with your move!

If it were me I might also plant the pots in the ground to help give them a constant temperature and keep them a bit warmer (the wind chill will be a lot colder for them than the ground temp) When you're ready to move just pull up the pots, if you have to move during winter you may have to put something to let you lift it out easier when the ground is frozen

One year I thined my peonies and had so many roots I could't give them all away. I threw them on top of my compost pikle and they all sprouted in the spring. John

Mine finally have a permanent home after a lot of moves and finally making it to my new house. I sure hope they spread like yours must have John. I put them at the end of the bed so I can add-on and have a mass planting of them.