If you drink one pound of water and pee it out do you lose a pound?

Your output would equal your intake so there would be no net change in body weight.

If you drink ice cold water, your body will burn some calories as it warms the water up to body temperature. You would burn 175 calories if you drink one liter of ice water.

3500 calories equal one pound. So if you were to drink 20 liters of ice water, you would lose 1 pound.