Gandalf on a white Mumak?

[Kyledanger]

Hello all, or should I say, "a star shines in the hou of our meeting"?
Anyway, long time lurker, first time poster. I figured that this would be the place to get some insight on something I have been pondering:

When Frodo and Sam see the Oliphant in the Two Towers, Frodo wishes that Gandalf was riding a white Mumak leading a thousand Mumaks to defeat Sauron. Now, by this time, Gandalf was already back as The White, though Frodo would not have known this.

So why a white Mumak? Just a symbol of good? When gandalf encouraged Frodo to take off the Ring on Amon Hen telepathically, was there some communication of his resurrection and change of wardrobe?

Perhaps this is over thinking it and reading too much into an otherwise simple wish by a weary hobbit... But that's sort of the point of this place.