This is an interesting subject, not discussed too often. Generally speaking, without trying to scare anyone, woodworking for some may not be very safe. Some of us are more sensitive to materials than others, and may react differently.
In working with wood, contact takes a few forms such as touching the stock, having the wood dust make contact with the skin, having the wood dust enter our body through breathing, eyes, ears, and mouth (any orifice really). If you "Google"
toxic woods, you will find many sites of lists of woods, charts, tests, and results of certain woods that have a potential hazard.
In my 37 years of woodworking on a daily basis, dry hands are not my only problem. Like I stated earlier, some people are more sensitive than others, and my exposure extensive. For those with chronic sensitivity levels (possibly unknowingly), once subjected to the source, the sensitivity gets more acute and chronic. I couldn't even guess which specie I'm sensitive to, but my hands are like sandpaper, and I have to use hand cream several times during the day.
Dry hands may not be the result of the physical contact alone, but could be a reaction to other forms of contact. Something like a side reaction. After several dermatologists, the best they can come up with is a case of dermatitis, which just about covers most skin irritations.
I'm also a cancer survivor. Detected in 2001, a close call with bladder cancer. Specialists attribute possible causes as inhaled foreign matter, including dust and chemicals, and direct contact with the skin.
Wood and its dust has the tendency to draw moisture from contact, much like talcom powder would do. The difference being that woods vary in their chemical properties. If you show an early sensitivity, you might consider seeing a doctor, and use precautionary steps like gloves, respirator, etc. Keep in mind it's nearly impossible to completely protect ourselves.