This redhead here is blonde when it comes to a hottub but when I read your post the first question came to me was how's your pH of the tub? Here in Colorado, in the area where I live, our water is not too hard, not too soft but it did take me a few days to get a handle on the pH. Once I got it in range, dry skin was not an issue at all.
I'm sure the experienced guys (and women too) know more about this...
Linda