White Reindeers in the LWW film.

"The reindeer were about the size of Shetland ponies and their hair was so white that even the snow hardly looked white compared with them; their branching horns were gilded and shone like something on fire when the sunrise caught them"
―Chapter 3 [src]

White Reindeer were the creatures that were used by the White Witch to haul her sledge. They were driven cruelly by the Witch's dwarf, Ginarrbrik, who used a whip to make them go faster.

They were described as above; large deer the size of Shetland ponies, a brilliantly white colour, with horns that shone like fire. 

They carried Jadis throughout all of Narnia until Aslan brought an end to her winter and they could not pull the sledge any further, after which Jadis, Ginarrbrik and Edmund Pevensie got out and walked. Jadis had Ginarrbrik cut the harness, saying that the reindeer would find their own way home.

These creatures were obviously bred in Narnia, though they never spoke, so it is possible that they were mere dumb beasts instead of talking Narnians.

Nothing else is known about them, and the only other white Reindeer spoken of was the White Stag.