Cold water doesn't have to be really cold to kill you and the water temperature can be 70 F and less and kill you even then.
But of course the colder the water the faster it will kill you if not rescued in time from the water.
Cold water even at 70 F can kill you within 20 minutes or so if you're not rescued in time and then hypothermia sets in.
You die when your core body temperatures drops below normal so it's possible for the water to cause hypothermia even when it's not that cold.
If you fall into freezing water it's very possible for the person to die within 5 minutes or less and some people die within 1 minute of falling into cold water.