I've thought about the symbolism of that bird quite a bit. My personal theory, and this is a rather farfetched one but regardless, is that Hyrule is a divided land torn by evil and ignorant of the myths of the Golden Goddesses. The bird in the logo symbolizes the hero, Link, from Skyloft, since Skyloft is close to the heavens, bringing the myths and blessings of the Golden Goddesses down to Hyrule to save them (the bird is carrying the Triforce in the logo after all, though whether that has symbolic purpose or is for aesthetic balance remains to be seen).
What I find curious is that the bird in the logo, though apparently made of gold, is imperfect. It is tarnished and cracked in places, perhaps showing a fall from grace for the people of Skyloft? Perhaps Skyloft suffered to save Hyrule, resulting in the semi-ruined state of some areas of the City in the Sky (yes I believe that Skyloft and the City in the Sky are closely related)? I'm just throwing out theories really, there might not even be a symbolic purpose for the cracked gold other than aesthetics, but hey, who knows? It's fun to speculate on such things.