Had this discussion after a game this past weekend.
All this time I'd been playing like asteroids and minefields only affected a single zone (all ships in a player's RED zone - but all of the rest of their ships were unaffected).
I play a lot of two player games, so this may just be the mindset I was in. I can't find rules that tell me either way - although it sure would make sense for it to be all of a player's ships (particularly in large games - mining a single zone of a single player in a 4 player game would seem quite lame).
The BGG forums refer to an answer on this forum, but I can't find it.