"Witches wear a long cloak and pointed hat."

FALSE.

Many Witches do have a long cloak for use outdoors, as it covers clothing and keeps the weather out. It's useful if you wear robes during ritual. A hood enables you to pull it up, step into the trees and become invisible to anyone but the most keen observer. This was useful when practicing Witchcraft was illegal and Witches were forced to hide and do their rituals at night when no one was watching.
The pointed hat, however, is not something many Witches will own unless they have a taste for fancy-dress parties.