Party Pete's Wig is a rainbow afro that appears randomly in wheat fields during the New Year's Resolutions event. One of the resolutions requires finding the wig, lost after a Saturday night of partying. Picking it up does not yield any items and it does not appear as a dot on the minimap. A message "You found Party Pete's Wig from Saturday Night!" appears and the wig then vanishes.
A good strategy to find the wig can be to hop worlds in one of the fields listed below, until you find a world where the wig is located in the field you're standing in.