The Harmony Day Festival takes place in Winter. On the 5th day, people give cakes to give thanks to people in their lives. This isn't a special sort of holiday, as it doesn't have a start or end time, and it doesn't not occur at a certain location.
The player will go around town with Shortcake for villagers that they want to befriend. Giving somebody a cake will increase your friendship with them. Anybody who is given a cake will accept the present as if it's one of their favorite gifts (even if they don't like Shortcake regularly).
The player can obtain Shortcake by making it in the oven. The recipe is: Wheat Flour, Egg, Butter, Milk, Strawberry. Alternatively, you can buy Shortcake from the Brass Bar for 2200G. Hayden's store must be upgraded to level 3 before Shortcake will appear.