What are the Sun signs of Dorothy and her friends from Oz?

My guess is that they all represent the four fixed signs of the zodiac. Dorothy is a Scorpio (strong, persistent, focused on her goal to get home, over coming her enemies), Cowardly Lion is a Leo (vain, pionate, wanting to be the center of attention but a bit insecure underneath), Tin Man is a Taurus (dependable, reliable.. his steady ax saving the day, and soft and sentimental deep down) and Scarecrow is an Aquarius (intellectual, thoughtful, humanitarian and mindful of making plans).