Shadowfax is a Mearh stallion and Gandalf's mount in the Lord of the Rings. He is extremely fast and can be ridden without tack, as long as the rider is Gandalf. At the end of The Lord of the Rings, he travels with Gandalf into the West.
Ignorant fanfic writers often make Shadowfax ridable by others beyond just Gandalf, or have Shadowfax sire another Mearh which is often intended to be a special mount and/or companion to a Mary Sue. Sometimes, they even have him put up with a saddle.