The stable has evolved and you can put on/remove tack from your horse by dragging it in the squares.
Clicking on tack will also display the information about that item.

Note for Firefox users: If Firefox crashes when you select your horse from the stable, you will have to upgrade it to the latest version (from www.mozilla.com)
There seems to be a bug in older versions of Firefox, since browsers should not crash because of a web page.