Shamrock Day is an event held in New Leaf on March 17th. On this day, the player can speak to Isabelle to receive the Shamrock Hat. Following up to this holiday, whether or not the player has the Beautiful Town Ordinance in play or not, they will find many clovers scattered about their town. The clovers are not considered to be weeds.
In the Animal Crossing series, the term "shamrock" is used rather than "St. Patrick's." After the player has received the Shamrock Hat, villagers will compliment the fact that they are celebrating the holiday. They will only say this once while they are wearing the hat.