Like the others have mentioned, try supplementing with some type of oil (fish, salmon, coconut, etc) and see if that helps.
My dogs sometimes get dry skin in the winter, I just load them up on salmon oil and it general resolves in a month or so!
Murdock - GSD
Virgil, CGC - GSD
Tara, Reagan, Madison, and Jefferson - Aussies
The birds: Dante - CAG / Nero and Sunshine - Budgies