The Reindeer of Halloween Town were created by Dr. Finkelstein for Jack to use during Christmas time. Santa Claus also has his own set of reindeer, which Jack's were modeled after, although Jack's are composed of the skeletons of reindeer instead.
 Kingdom Hearts II
The reindeer play a small role in Christmas Town. They are only seen twice, once with Santa Claus, and once with Jack Skellington.
Santa Claus' reindeer have light tan fur and black hooves. They all have long snouts with a small, spherical, red nose on the tip. Their antlers are brown and vertical, and they all wear a green wreath decorated with a gold bell and several red berries around their necks.
Jack Skellington's reindeer are completely skeletal, with white bones and black hooves. They have their own, dark grey wreaths, decorated with golden spheres and a faded red bow on the top of each one. Their antlers are crescent-shaped and face inward.
In The Nightmare Before Christmas, Jack's skeletal reindeer take him around world to deliver presents, but they are shot down along with his sleigh by the military.