Frederik was seen wearing a tartan-patterned jacket with a blue scarf underneath and red sunglasses.
While most of the family had made it to Queenstown, Prince Christian, 18, was reportedly remaining in Denmark to finish his studies.
The future King and Queen of Denmark and their children have not yet been seen on their holiday together as a family. Mary, who is from Tasmania, has been avoiding speculation from the media in recent weeks.
Spanish magazine Lecturas published photos of Frederik with Mexican model Genoveva Casanova at Pablo Picasso’s art exhibition in Madrid early in November. The two had also been seen exploring the city together, sparking rumours of an alleged affair.
However, Casanova quickly dismissed the rumours in an interview with Spanish magazine Hola!: “I flatly deny the statements that suggest a romantic relationship between Prince Frederik and me.”
“Any statement of this type is not only completely untrue but also distorts the facts in a malicious manner.”
The Danish royal couple have since responded by presenting themselves as a united team and family, with a video uploaded to the family’s Instagram account in early December which showed Mary and Frederik decorating their Christmas tree with the four kids.