Possible Clues:

• It's called a caribou in North America
• Santa’s team
• Eg, Prancer and Dancer
• Northern resident declared showers overpriced
• Package deliverers of the present day?
• If an animal with antlers is female, it must be a ____
• Check on what sounds like expensive animal
• Member of a popular package delivery service
• Prancer or Dancer, say
• Tundra herbivore