I remember reading that when the wolf appeared, and I think it was implied (but never confirmed...) that the White Wolf is Link's father.
HIGHLIGHT ABOVE (SPOILER)
I also thought that the guy who teaches you new moves, dressed up in all that metal get-up could be the white wolf, link's father, in human form.
HIGHLIGHT ABOVE (SPOILER)
Apologies, I have no idea how to do the spoiler tags.