For me dry skin isn't much related to diet. I had my water heater blow
out a few years ago in mid-winter. The landlord didn't get it fixed for
several weeks, so I took the shortest, coldest showers I ever had. In
that time my dry skin completely disappeared. It came back within a day
or two of getting my water heater fixed.

Now, I take cold showers as long as the weather permits, and keep the
shower temp as low as I can stand in winter. It makes a big difference,
but still, my skin gets dryer as soon as I start using warm water in
the fall.