I think this was just an off duty appearance; Country Kate in her tweed suit goes to church with the family. staff deserves time off over the holidays too.
i think in their own way the Cambridges are trying to be accessible
The Duchess' hair seems just fine to me. Neither frizzy nor unkempt. It is shiny and bouncy as usual. Keeping it straighter than usual is perhaps not a unpardonable sin.