Divide & Conquer timing?
Spring as they poke their little heads up, of course. Have done late spring divisions for gifting to other Hosta growers. I prefer to divide hostas that are overgrowing their spot in autumn. My thinking is to get them to establish roots before freezing weather. I've had good luck with all of these times as long as they get replanted right away.
I'm open to learning from experienced growers, though. What is your preferred time to rework hosta beds?