Pony Time actually reminds me of the hard-boiled egg from the revolutionary rallying cry in another Terry Pratchett story.

Part of me feels a little sad that they set it aside if I understand your story correctly. Real world politics is rife with this kind of tradition for tradition's sake. It's one of the things that ends up binding people together in the long run. Compare and contrast The Black Rod in the British Parliament and their role in summoning the Commons.