First off, you can not put chests in horses. You will need to find a donkey varient. Donkeys are recognizable with their long ears. Then click the donkey with a chest.
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If you have the chest slot empty in your armor inventory, Shift click or drag the Elytra into the chest slot.
After taming the horse and adding a saddle to it, you can add a chest by left or right clicking the horse, I forget which. Upon death, the horse should drop the chest and the contents of the chest.
If you go into sneak mode (hold left shift) and right click on the horse, you will open its inventory so you can equip it with horse armour and a saddle.
You cannot place a chest on a horse.You can however, place one in the inventory of a Donkey.Simply sit on the tamed donkey and press E.This will open the donkey's inventory.Place your chest in the box that has the silhouette of a chest.
how do you tame a horse in minecraft 1.7.4?