Variously, as 'silver' or 'grey'.
It could well have been Tolkien's intention that he meant Shadowfax to be what most people would wrongly call a 'white' horse (he was a clever bloke after all... and was probably well aware of the grey/white conventions of horse colourings!).
But, as I've always said, Shadowfax would be a stupid name for a 'white' horse.
Also, Tolkien described the name Shadowfax as an anglicized form of Old English Sceadu-faex 'having shadow-grey mane (and coat)'.
And while equine-parlance is one thing, Tolkien in his books describes certain horses as white (Asfaloth for example), but Shadowfax is always "grey" or shining like silver. So while a "grey" horse can look white to the eye (considering equine-parlance), should there not also be some colour distinction between Tolkien's horses -- between those which are white (and look white to the eye) and others who are grey, especially "shadow-grey"?"A great dark-grey horse was brought to Aragorn, and he mounted it."
This is Hasufel, Old English hasu "dusky, grey, ashen" "... but their captains and chieftains were upon horses, white and grey."
Of Tuor And His Coming To Gondolin, really the unfinished Fall of Gondolin
from the early 1950s, Unfinished Tales
I don't doubt that Tolkien was aware of horse parlance, but I still think he meant to draw a distinction in colour (to they eye) between his white and grey horses.
He said... ah... a bit late to the conversation