High-headed is a term used to describe someone who is arrogant or snobbish. There are several synonyms for this term, including haughty, conceited, proud, and pompous. All of these words suggest a certain level of self-importance and disregard for others. Other options include lofty, overbearing, imperious, and supercilious. These words are often used to describe individuals who believe themselves to be better than others due to their wealth, social status, or other perceived advantages. Regardless of the exact term used, someone who is high-headed is unlikely to be well-liked by those around them.