Only seen in the Santa's Sweatshop DLC. They appear to have little function, but can be picked up similarly to a desk. They will occasionally walk around. The starter job claims of cleaning reindeer manure.
You will not receive heat for carrying them, unlike desks and fallen guards/inmates.
If you are put in solitary while carrying a reindeer, that reindeer will be stuck floating above your head until the game is reloaded. You can, however, still pick up and drop objects normally.