As a wizard, he had the ability to be ... a cloak and a wide-brimmed hat, which influenced Tolkien's descriptions of Gandalf. However, unlike Odin, Gandalf served higher powers: Eru Ilúvatar ...

and he never covers it with a hat. Gandalf still has a beard, which has also turned white, but it's much shorter than in his Grey form. A wizard's staff is a mighty weapon, an important tool that ...