Scurf/dandruff in elderly dog

Have you consulted a vet? A blood test showed that my dog has an under active thyroid - medication has made a huge difference to her coat.

Might it be because of winter and having the heating on? My Whippet loses a lot of hair in winter which grows back in the spring. At least I hope it does this year. We call her Baldy Bum. I’m adding fish oil to her food and a bit of porridge. Not sure if there are any medical conditions in older dogs that might cause dry skin though.