The minis were awesome. Lucy, Fred, Ed, and Tiny Tim were kind and docile, and jumped out of their trailer ready to eat grass. They let toddlers pull them around on leashes, and all was calm except for a moment when Lucy sauntered off into the backyard. The boys joined her, and when they realized they were all loose, they began sprinting in circles, kicking up little clouds of dust. It was funny, and then we got nervous, and then they were corralled and we could laugh.
So yes. Miniature horses can stampede.
I hope we get to add one to the farm soon. Don't you love the picture above where you can't even tell which end is which on the mini? Glorious manes.