I'm surprised this took so long. I had to use regular furries in my game! The outrage! I did have a pony mount I think though if I remember correctly?
Anyway, a moddder named Kakujoey over on Nexus Mods is currently working on bringing our cartoon horses to Stardew Valley, starting with Pinkie Pie, Twilight, and Fluttershy so far. It's a simple model swap, so nothing too complicated.
Go grab it here.