How long you survive in cold water depends on a number of circumstances.
Water temperature: The experts define "cold water" as anything below 70 F (21 C). That might seem somewhat warm, but the reason they use that number is because that is the water temperature in which you can maintain your body temperature more or less indefinately. Below that water temperature, your body will gradually loose heat and you will eventually become hypothermic. How fast you become hypothermic obviously depends on how cold the water is. You will live longer in Florida than in Alaska.
Flotation: In cold water, you loose strength and dexterity in your arms and legs long before your core becomes hypothermic. When your arms and legs give out you can no longer swim or tread water. Without a life jacket you will drown long before your core becomes hypothermic.
Gender and body type: There are small differences due to gender and body type. Skinny people get hypothermic slightly faster than well padded people. Men typically get hypothermic slightly faster than women. These differences are generally very small however.
This has led to the One:Ten:One principle for very cold water.
"One Minute" When you fall in cold water your first reflex will be gasping and hyperventilation. This can last from seconds up to a minute. Your first priority is to get your breathing under control and to not inhale any water.
"Ten Minutes" In really cold water you have about ten minutes of useful motion to save yourself. You can swim, grab a lifeline, etc. After about ten minutes you will no longer have effective use of your arms and legs, and without floatation you will drown!
"One Hour" With a life jacket, it will take at least an hour before your core temperature drops to the point of dangerous hypothermia. (Even in the coldest water, some people with life jackets have been successfully rewarmed even after a couple of hours.)
One:Ten:One is obviously an average, and assumes very cold water like we have in Alaska. In other areas, like Florida, the "One Minute" gasping reflex might be shorter, or not happen at all. Likewise the "Ten Minutes" of useful motion and "One Hour" time to hypothermia might be much longer.
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"Toto, I've a feeling we're not in Kansas any more."
-Dorothy, in The Wizard of Oz