And now for the answer!

Y'all are pretty darn clever, the answer was teeth. However I'm not sure why y'all were guessing all these other critters... sheep, goats, cows, a carnivore, squirrel, opossum... Seriously?  C'mon you know me, they're horse teeth!!
Really and truly they are.  The chew tin had mostly wolf teeth and bridle teeth.  Some were cut off and some had the roots, which would probably be why some appeared canine like.

Dale the horse dentist was out last week.  He is a pretty cool guy.  I love that he hand floats and takes his time to really check the horse out and make him/her comfortable.  I also love that he doesn't just reach for the drugs to 'help' the horse cooperate, he'll give them a chance without it first.
The stories this guy has, wow!  He's been involved in horses pretty much all his life (he's in his late 60's)  He's shown horses, been a farrier, bred & raised horses (actually he still does some of that)
Every time Dale is out I learn something new from him.  Sometimes its something practical, like a colt handling tip he demonstrated with Tavi.  Sometimes its something that comes out in a story, like horses can get addicted to pain killers (that was a pretty funny story actually)
Dale collects teeth and he pulled some of his collection out to show us.  There were those teeth in the tin and a bunch of others as well.  Some of them had a story, some didn't.  The one below came from a Welsh pony stallion:

That was a bridle tooth.  Normally Dale would have left it alone, or if he were to do anything he would have cut it down.  But in this case you can see the whole root came too.  Take a good look at it.  The "shiny-ish" small section on the left is the tooth.  About where it curves is where the root starts.  See those holes and all those grooves etched in the root?  Poor little stud had a very bad infection in that root, which is why the whole thing got pulled.
Teeth can cause all kinds of issues.  They can manifest in how your horse behaves under saddle, his ground manners, how he keeps weight on (or rather doesn't keep weight on)  Some horses are pretty stoic though and don't give you a lot of clues.  Also your horse can't tell you when he has a tooth ache so its a good idea to get them at least checked regularly.