The down side to cold water is its shock to your body. It's better for digestion if you don't drink cold water.
Cold water increasing metabolism is negligible unless all the other methods to increase metabolism are followed: eating healthy protein, fueling your body often, strength training, cardio, eating whole foods, fluctuating calories, healthy fats and complex carbs. It's the combination not the single method which works.
I know because I finally sweat upon exertion and doing cardio. I didn't when I first began because my metabolism was cr*p! I gained weight eating 2 meals a day! It isn't cr*p now!
I followed everything above for the past 6 months and it took most of that time to boost my metabolism to it's natural fat burning high.