Shadowfax was the King of Horses, a steed of the Mearas of Rohan. By day his coat was silver, and by night like unseen shade.

Théoden initially allowed Gandalf to borrow Shadowfax reluctantly, but after Gandalf freed the King from Gríma's influence, Théoden gave the Mearas to Gandalf gratefully.

Shadowfax would take no saddle or bridle, and would only carry those who he wanted to carry. It is thought that he sailed into the West at the end of the Third Age with Gandalf.
Encyclopedia entry originally written by Hathaldir