Lyrics are found in
The Annotated Score
of the Two Towers.
Shadowfax's Arrival at
Fangorn as heard on the
OST and the White Rider's
arrival at Helm's Deep use the same melody. But the Fangorn scene
was replaced with an alternate composition still using lyrics from
The Mears but with a different melody.
In an extended TTT scene, Gandalf talks about Merry
and Pippin being two small stones. Singing is heard in this scene
that apparently utilizes lyrics from The Mearas because of it's
proximity to Shadowfax's arrival at Fangorn. This scene has nothing
to do with Shadowfax nor does it have a reason to use Rohirric
lyrics but I have it on good authority that it was, in fact, lyrics
from The Mearas that was used.
The London Voices and Ben del Maestro.