Wiley,
Here is a link to cold water survival times, table at the bottom of the page.
Cold Water Survival
The main point to take away is that survival time is greater than the time to exhaustion or unconsciousness, which is where the life jacket comes in. It should keep the head above water, make it easier to locate the person in the water and also gives something to grab hold of.
Another interesting point from the site
Swimming or treading water will greatly increase heat loss and can shorten survival time by more than 50%.
Gotta love Google