I expected the horse to move one tile for each block you placed. I had an elaborate plan to lure it towards one exit and then close it at the last minute... Nope!
I did see a game recently which did that (you place a tile, the animal moves a tile, etc.) - possibly on itch.io. I'll see if I can dig it out.
John Conway studied similar problems
https://en.wikipedia.org/wiki/Angel_problem