What has happened to my peonies?
This is powdery mildew, a fungus. It has become more of a problem in the past few years on peonies. At this time of year there is no point in spraying a fungicide.
The most important thing you can do now is to cut the foliage to the ground and pick up any dropped leaves and dispose of them after it browns from heavy frost. This will reduce the amount of infectious material which could reinfect the plant next year.
Next year, as soon as you see any white infection, remove the infected leaf and spray with a fungicide labeled for powdery mildew.