'There is more than one horse coming,' said Aragorn.

'Certainly,' said Gandalf. 'We are too great a burden for one.'

'There are three,' said Legolas, gazing out over the plain. 'See how they run? There is Hasufel, and there is my friend Arod beside him! But there is another that strides ahead: a very great horse. I have not seen his like before.'

'Nor will you again,' said Gandalf. 'That is Shadowfax. He is the chief of the Mearas, lords of horses, and not even Theoden, King of Rohan, has ever looked on a better. Does he not shine like silver, and run as smoothly as a swift stream? He has come for me: the horse of the White Rider. We are going to battle together.'
photo from www.TheOneRing.net
SHADOWFAX
in J R R Tolkien's
THE LORD OF THE RINGS

"a horse that might have been from the earliest time of the world. No man had ever ridden him before. By day his coat was like silver, by night like unseen shade. His footsteps were light, and not even the horses of the Nine were his match for speed or stamina."

Shadowfax chose his rider,  needing neither saddle nor bridle. 
The andalusian stallion Demero is Shadowfax in the movie
Shadowfax and Gandalf at Helms Deep - in "The Two Towers"
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