Tree and herbaceous peonies are winter-hardy plants that overwinter in garden soil down to USDA Zone 3 climates. In climates colder than this, peonies grown in containers can be overwintered indoors and kept cold. Peonies require a fairly long cold period in winter to break dormancy and set the bloom for the spring. Ambient storage temperatures have a ceiling of 40 degrees Fahrenheit and can safely be much lower. In climates where winter temperatures are mild and hover around 40 degrees or higher, cold storage in a chilled room or refrigerator may allow you to grow peonies in warmer climates beyond their natural range.
Overwinter your peonies in the garden soil in USDA zones 3 through 10a. Mulch around the base of the plant in climates where their top foliage overwinters intact. Mulch over the sheared crown of the plant in climates where the top foliage does not overwinter. Lay down a blanket with a layer of organic mulch that's at least 3 inches thick, to insulate the roots from cold, drying winds and drought. Use compost, leaf mold, shredded bark or cocoa bean hulls for the best insulating effect and soil building benefits.
Store potted peony plants growing in USDA zones 1 and 2 indoors over winter at a temperature below 40 degrees Fahrenheit and above -40 degrees Fahrenheit. Allow for some fresh air circulation and access to daily sunlight if possible. Keep the soil lightly moist but not wet.
Overwinter peonies growing in the warmer climates of USDA zones 9b through 11 in a cold room facility or a refrigerator for a period of at least 30 days to break the dormancy period and trigger the buds for bloom. The preferred method is to store the peony plant in its pot without disturbing the roots and keeping the soil very lightly moist at all times.
Digging up established ground-planted peonies to chill them is never recommended, as they are extremely averse to being moved and can easily be killed by damage to the roots. Even with careful relocation, peonies will need multiple years to reestablish themselves in the soil before bloom--so annual movement is not possible.