I kinda think of peonies like trees or shrubs and just leave them be. Of course I'm thinking of my grandmother's peonies that were just out in the lawn and stayed there forever undisturbed. I do care for them more than she did (she loved her flowers, but wasn't really much of a gardener per se). Then I've never gardened in one spot for more than 10 years, so my old varieties I've carried with me haven't really gotten a chance to develop huge clumps.
Tracey and Diann, I'm curious how you decide on time to divide?