Exactly what it sounds like, you cannot breed any horse wearing armor although you can breed a donkey with a chest which is correct.
MC-15442
Horse Armor Prevents Breeding
Resolved
Duplicate
0
Wool Dye
(Unassigned)
Unconfirmed
armor, horse
Snapshot 13w19a
Retrieved
Duplicate of MC-13899, please use the search function to see if your bug has already been submitted. Currently over 55% of tickets are being closed as duplicate.