The issue with training reeks of bug. I'm doing playtesting for a Cats guide, and just adopted an Elder. She had no hunter trait and no previous experience hunting. I got her toy, and after I clicked it to tell her to practice, she quickly gained two levels. She was sent outside for some stalking, and not only grabbed a few more levels, also adopted the Hunter trait. So, you can teach an old cat new tricks. Don't know about dogs yet
I'll update this post with the results of elder dog training in a few.
Edit: Dog learned the skill fine, thankfully. What is odd is that I can't get him to take on the hunter trait. After one attempt at hunting I was able to praise him, which should help, but the option has disappeared entirely no matter what method i use to get him searching.