Well, the mearas according to legend were brought from the West by Orome (or
Bema as he was known in Rohan), and Shadowfax is said to have crossed back the
the Undying Lands with Gandalf at the end of the Third Age. So I will go
out on a limb and say that the mearas could be some kind of Maiar horses,
perhaps like the giant eagles of Manwe who are more than regular eagles.
If Shadowfax has such a divine origin, no wonder he can defy a winged Nazgul
Lord!
Shadowfax standing as steadfast as the graven images makes me wonder if Tolkien
is implying that there some kind of ageless, immortal (??) dimension to the
horse.
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Still round the corner there may wait
A new road or a secret gate;
And though I oft have passed them by,
A day will come at last when I
Shall take the hidden paths that run
West of the Moon, East of the Sun.