Is it possible for a cold water pools water volume to increase due to condensation of the surrounding water vapor And is it easily calculable?

second law of thermodynamics dictates that a mixture of two diffrent temperature makes an equilibrium.

And heres the problem, in a normal environment, the cold water pool and its environment are in equilibrium. That is to say when cold water is supplied to the pool.

Why is that? The temperature of the environment (which is infinitly large) is higher than the pool (finitly large). In order to obtain a vapour (which is needed for condensation) the water must rise a significant temperature. It is known that the water at 1 ATM (1 atmosphere; 1.15 bar) should be arround 100 oC to boil. Naturally water starts to evaporate much earlier.

However, water will not evaporate, as you said before, the water is cold. When the water is very cold and the environment is very cold. The gas, which is in equilibrium, will condensate, but WILL stay as small droplets in gas as a vapour on top of the water. It cannot be considered as part of the pool. Futhermore this layer will evaporate as first when the temperature rises.

SO the answer to your question is no, the pool water volume cannot increase under normal conditions