In this generation, the Equestrian equivalent of Christmas is actually called Christmas. it would later be called "Hearth's Warming Day" in G4 and "Winter Wishintine's Day" in G5. the words "Christmas" and "Santa" would not be used again in the franchise until the G4 Christmas album "A Pony Kind Of Christmas".
This is the first Christmas special of the franchise, followed by G4's "Best Gift Ever (2018)" and G5's "Winter Wishday (2022)"