I'd use a green twig, or a twig that recently fell for this craft. I tried dried out ones, and they crumbled when I drilled them. You'll need a twig to cut the body, and a head. Then a smaller twig for 4 legs and a neck. An even smaller twig with branches coming off for the antlers. Drill the holes you need and glue them to make sure they don't fall apart,lol! These would look cute as a table top decoration or set in a potted plant!
Here is a link that might be useful: Kudzu's Blog