Choke can be scary. I never feed treats in their grain. Always as part of training (even if it's simply the head down cue) I make sure they are done with what's in their mouth before shoving in another...
Yes, I have a medium and large. All of my horses (minis included) will go attack them when I give the cue "play ball". Sometimes when they are bored and they see I am watching them they will do it themselves and then look at me, ears up listening for the bridge sound....