Hobbyhorse - n.
1. a pet idea or project
2. a stick with a horse's head or a rocking horse, ridden by children
3. a figure of a horse, attached at the waist of a performer in a morris dance, pantomime, etc.
And that led me to look up Morris Dance:
Morris dance is a form of English folk dance usually accompanied by music. It is based on rhythmic stepping and the execution of choreographed figures by a group of dancers, usually wearing bell pads on their shins. Implements such as sticks, swords and handkerchiefs may also be wielded by the dancers.
If I had ever heard the term, and it seems likely, I had long forgotten it.