Normally only abut two minutes before brain damage can start setting in, though body temperature has a lot to do with it. There are instances of people who have been immersed in icy water and stopped breathing, but who have been resuscitated after some hours.
'Free' divers can hold their breath for up to about eight minutes, but that not the same as being without oxygen.
The condition Heathfield describes with icy water is called mammalian diving reflex. You get it in humans to some extent. but especially in marine mammals. The heart rate slows and blood is concentrated in the vital organs as a response to the head being submerged in cold water.
Again if the brain stops getting any oxygenated blood at all damage happens very quickly