Here's what happened:
* Miami Vice won a Golden Globe Award for Best Television Series - Drama in 1985.
* Edward James Olmos played the role of Lieutenant Martin Castillo in the series.
* Don Johnson who played Sonny Crockett, won the Golden Globe Award for Best Actor in a Television Series - Drama in 1986.
So, Olmos wasn't individually awarded a Golden Globe for his Miami Vice role, but he was part of the winning team that brought the show its accolades.