Dry skin is really a function of water hardness and how long you stay in the water. Any amount of soaking in water, no matter the exact chemistry, will cause the natural oils in your skin to be washed away. Once you exit the pool and towel off, your skin has lost a lot of the essential oils in it that protect it from dehydration. This is what causes most problems with dry skin. High hardness water (high TA and CH) causes the formation of calcium stearate and other kinds of calcium based "soap scum" to form on the skin. This is why people feel "squeaky" clean after showering in high hardness water - the calcium deposits on the skin don't allow for soap to do it's job well at removing dirt and dead skin. So the "squeaky" skin feel is actually skin that is still a little dirty and has calcium deposits on it. In softened water, people will often feel that their skin is slippery and think they did not wash off the soap properly. That's actually skin oils coming out and how your skin should feel when it's clean. Stay in a shower or bath too long and you exhaust all the oils in your skin and you'll feel very dry after a shower too.
In a commercial pool, you're not typically bathing long enough to have the same effect and there's also a lot of oil in the water from other bathers. Believe it or not, the fact that your skin doesn't feel dry is probably an indication that the water is loaded up with bather waste and you're simply not losing as much as you would in an otherwise clean pool. Yuck.
One way to help with dry skin around a pool is towel off after swimming and then apply a very light skin cream/lotion in order to restore essential oils (creams with Vitamin C help eliminate chlorine if there's no shower available). Using a cream with a small amount of sunblock in it (10-15 SPF) helps to keep sun burns away.
