In "Cinderella," the magical tree and bird are Cinderella's magical buddies. Supposedly she's a "good" and "devout" (25) girl, and so maybe she deserved this supernatural help, but Cinderella would be nothing in this poem without the constant aid of magic. The poem uses the supernatural as a kind of extended metaphor for how frustrating Cinderella stories actually are. Practically everything is handed to the heroine with no work involved on her part. No fair-sies! The example stories in the beginning are a little different—they don't involve the supernatural—but there's an element of supernatural intervention to them anyway. (Read more about this in the "Luck/Fortune" theme.)
The white dove in "Cinderella" is a complicated little bird (like Tweety, but way deeper). It represents both compassion for the needy, but also a free hand-out that no one deserves.
Nice try, but the supernatural forces in this poem don't actually help Cinderella at all.