Tolkien never states explicitly that Shadowfax sailed into the West. In his Letters, though, he gives such a wealth of clues and hints, we can state with near-certainty that the great horse sailed on the White Ship with his master Gandalf. (See The Letters of J.R.R. Tolkien, No. 268, dated 1965).

Fax is an extinct word for 'hair' or 'coat', now only surviving in a few place- and family-names, like 'Fairfax'. In fact, Tolkien has anglicised the name 'Shadowfax' somewhat from its original form; in the Old English language representing the tongue of the Rohirrim who bred him, he would have been called Sceadufax or Scadufax.