Thanks to +Nobilis Reed for pointing this out to me on Facebook.
A company called Megasus Horsetech, which is based in Germany, has started making something they call "Megasus Horserunners" which are basically rubber, clip on horse shoes that resemble sneakers. They believe these are better than traditional horse shoes. (And like many people who say that claim nailing on shoes hurts the horse - it doesn't unless somebody screws up).
So, are running shoes for horses a good idea? My personal jury is out. Temporary horseshoes are far from a new thing, but most horses that need shoes...need shoes. And this system seems finicky, with tape and such - traditional hoof boots are probably better.
But it opens up the question of what might happen with horse shoes and technology in the future - and I'm not sure. We haven't changed, significantly, how we shoe horses in centuries.