The term ONE ON A HIGH HORSE is used to describe someone who is arrogant and self-important. This term can be broken down into two crossword solutions: PRIG (4 letters) and SNOB (4 letters). PRIG is an old-fashioned word for someone who is excessively moralistic and prim, while SNOB is a more modern term for someone who is overly concerned with their own social status. Both words are used to describe someone who is haughty and superior in attitude.