I can't say I've noticed about my hair doing that because I have always washed my hair everyday for years anyhow. I know some say that you shouldn't do that, but I use hair products so I like to wash it out. I haven't noticed any damage to my hair either... my hairdresser sees me every 5 weeks and tells me how healthy my hair is and I have a lot of it. I don't use conditioner on my hair because the hair products I use puts oils in my hair. I have naturally fine and soft hair too so I don't need that. I used to use it years back and found it put too much oil in my hair and it was difficult to handle. I used to have long hair and I'd break a lot of things in my hair for that reason.. too soft, too thick, and oily from the conditioner. I'd wind up using a tonne of hairspray trying to get clips to stay in my hair.
I do suffer from dry skin though and I have never thought about what the cause of that is. But I need to moisturise more often than I used to when I was younger. My feet and legs tend to dry out the most. I've always moisturised my face, neck, etc... so they're usually ok.