I have always divided and moved my perennials in the spring as I worried about the frost popping the plants out of the soil if they were divided or moved in the fall. Is this faulty thinking? When is the best time in the fall to divide and move the perennials?
Fall is a great time to divide many perennials, particularly because the plants are still vigorous, the soil is warm, yet the air is cooler and often moister, so the divided plants will benefit, and be less stressed. Some plants are easier to divide than others, particularly iris, peony and hostas, as they have visible break points due to shallow and large tap roots or, in the case of hostas, growth points. Others have wide spread rooting systems, and can just be cut at advantageous points.
September to early October are good times to divide, as there will be plenty of time for the plants to start re-establishing roots before dormancy. Remember to provide a proper size hole to spread the roots, and the proper depth for plants such as peonies and irises. Tamp down gently then, water well. Some people use a root stimulant fertilizer or mulch with compost. Keep the newly divided plants well watered before freeze up. They will go dormant and be ready for spring.
For excellent advice on dividing perennials: Janet Macunovich writes in Fine Gardening: https://www.finegardening.com/10-tips-dividing-perennial-plants