Here is one example of Clay Chicken
that will give you the basic idea.
We did something like this years ago when I was a kid and went hunting with a couple of uncles and cousins - we just used clay that we dug up and added enough water to get it plastic enough we could use it (kind of more like thick clay mud) and then just covered the birds, feathers on, with the clay and baked them in a pit full of coals. When we pulled the clay off it pulled the feathers off with it. At least that's what I remember ... it's been about 45 years or so.