Event animals are animals that could only be obtained through a limited time event and most can only be bought with the special currency of the time before being present in the wild. Some event animals can be obtained in other manners depending on the event, however, can still only be found during a limited time event. These animals are not released permanently.
Once they have been purchased they are found in an identical manner to regular animals. To get the baby animal, the player has to search in the stampede for a 'match' after the adult has been purchased, and ride the 'match' for a specific amount of time to begin breeding the baby. Once the event expires, the player can still obtain the content from that event in following events, most namely, the next anniversary event, which is a chance to catch up on any missed animals and hats.