After decapitation, I did my best to sew all the tears closed. Some of the fabric was in pretty bad shape, and obviously, most of the beard and mustache are missing (Tibetan lamb on the hide must have been too tempting for the doggy).
After taping the hat and hair out of the way, I painted on a good layer of white tacky glue.
Next came a base layer of paperclay. I deliberately avoided the bottom of the head where it will be sewn to the body.
Here's what this Santa looked like new. I adapted "Cyrus the Summer Santa," a pattern by Rusty Needle Originals by Two Jays: