What is the word for someone who sees music as colours?

The general term is synesthesia, for any combination of senses (laymen also sometimes speak of "intersensoriality"), and sound-color synesthesia, or chromesthesia, for sounds and colors in particular.

Chromesthesia or sound to color synesthesia is a type of synesthesia in which heard sounds automatically and involuntarily evoke an experience of color

chromesthesia is a specific form of the general synesthesia and is a neurological condition in which stimulation of one sensory or cognitive pathway leads to automatic, involuntary experiences in a second sensory or cognitive pathway.