From the Super Mario Wiki
The Hollijolli Mayor is a Toad and the leader of Hollijolli Village. During the Shroob invasion of the village, the mayor attempts to hide from the aliens but ends up getting stuck in his chimney. However, Mario and Luigi, who have traveled through time to the past, help the mayor out of the chimney. Unfortunately, as soon as he is saved, the mayor of Hollijolli Village is abducted by Shroobs and presumably taken to the Toadwood Forest.
The Hollijolli Mayor has a white beard and wears a big, red coat. As such, the mayor resembles Santa Claus, a fitting allusion for the Christmas-themed Hollijolli Village. Additionally, his quirk of getting stuck in his chimney was likely a reference to Santa Claus's association with going down chimneys to deliver gifts.