Where did the term horse play is fools play originate from?
That exact term doesn't seem to be defined anywhere, but "horse play" probably originated from the way young horses frolic and play-fight. It's just silliness and fun with no constructive purpose. So perhaps it was thought that anything a "fool" engaged in was similar to "horse play" and was frivolous.
Horse-play is a term to describe rowdy, playing behavior. Ten examples of horse play include, pillow fights, jumping on the bed, playing baseball in the house, play fighting with siblings, or friends, ringing a doorbell and running, poking a friend with pencil, taking the dogs toy and running off with it, jumping over trash cans, climbing trees, and climbing on cars.
Yes, the term April Fools is a proper noun because it is a specific day of the year. The noun April itself is a proper noun the name of a specific month. The noun fools, the plural form for fool, is a common noun unless used as the name of something like April Fools Day. Some other examples are the song, 'Only Fools Rush In' or the movie, 'Ship of Fools'.