I have done it in the fall and I have done it in the spring as well. The plants seem to do better when I do my dividing in the spring. They don't seem to do as well wintering over as when they have all growing season to adjust to their new spots in the garden.
I do my dividing in the fall. I can see the plants so I know which ones need separating, plus it gives them a chance to get settled in before the spring thaw. By the time the snow melts in the spring, most of them have already started growing.
I didn't get around to it in the fall, so spring it is for me. I think I will transplant some to other places and then see if some of my friends want some of what is left.
I've divided Hostas and day lilies other than that I just leave my plants. I have to divide my Hostas because they grow like crazy. How do you keep those things from spreading all over your flower beds?
Perhaps planting them in a huge pot with the bottom cut out of it would help. I have done that with peppermint and stuff to prevent them from spreading.
Just another thought---the best season to divide plants can vary a little from plant to plant. If you have a good gardening book, the book will tell you the best time to do it.
I separate and divide plants when the clump gets as big as I want it to or it gets too crowded. Usually, I do it in fall because I'm too busy with the garden ad other things in the spring.