Source: The Great Interpretation of Dreams (Ibn Sirin)
(By analogy with a cap and turban) A hat in a dream indicates exaltation, prestige, and authority, or a husband. Its beauty indicates a good situation. Its falling indicates loss of position or worry.
Source: Perfuming Humanity in the Expression of Dreams (Al-Nabulsi)
(By analogy) A hat indicates travel, marriage, or protection. Wearing it indicates achieving one's goal.
Source: Signs in the Science of Expressions (Ibn Shaheen)
(By analogy) A hat is interpreted as prestige and position. Whoever sees himself wearing one, his status will rise.