I've had dry skin on this diet, which is something I've never suffered from before in my life. my lips got so dry at one point that they bled! And I drink between 2 and 4 litres of water a day, so definitely getting enough fluids.
I also get dry skin. I get it normally, but thought (wrongly) that drinking 4 litres of water a day might improve it!
My lips are extremely dry - which I think it related to the diet as I do not normally suffer with this.
It may or may be nothing to do with the CD plan. Weather, central heating, age etc all can contribute to dry skin and once it gets a bit dry it gets much more noticeable very quickly. Make sure you exfoliate in the shower (e.g with a shower brush and gel) to get the dry skin surface layer off so any moisturiser doesn't just sit on top of that.