Ahaha! I also love the rearing pose ponies, but you're right, they can be difficult to display, and while I was meticulous about keeping things together when I was a child, my parents probably would have thrown it away, thinking it was a piece of packaging. I think it would have been neat if they'd made the stands a bit more interesting (for example, a lot of Breyer horses have themed stands; a racetrack ground for the Smarty Jones mold, a brick wall jump for the Jumping Horse mold, etc).
I can't tell you how many times my Magic Star has fallen off her shelf >u< I'm lucky enough that my Skippity Doo came with her stand from her previous owner.
If you're in need of stands, though, I can direct you to
Clipper's e-crater, where you can buy replica stands