Ooooooooooh, I see now!
I still don't exactly agree though, only because Odin has never been equated with his horse, Sleipnir, in Final Fantasy. Neither has he been an elemental aeon/summon/GF, as Ixion was. Also, we could get into little details about creature design, how Sleipnir has always had 8 legs while Ixion only has 4, but that doesn't necessarily mean anything (especially considering how Odin's horse-form in XIII does, indeed, have only 4 legs).
I think Square has always made Odin unmistakeably Odin, up until XIII anyway, and that was only because of the whole vehicle function of the eidolons.
If anything, though, I think Odin's horse-form in XIII is a rendition of Ixion...but I don't think the same could be said of Ixion as a rendition of Odin (if that made any sense...it's late, lol).
But I'm gonna stop, because this is getting waaaaay too analytical, lol (sorry about that....I wrote an essay on FF summons once, I don't think I should do it again, haha)