I was testing out the horse breeding and when i tried to breed a horse with a saddle with another one that didn't work. So i spawned another and didn't put a saddle on it, then tried breeding it with the other horse without a saddle and it worked. Also tried it with no saddle but armor and it also doesn't work.I haven't tested this on a server but this just seems to be unimplemented so i imagine the bug would be there too.
Update-13w17a
Now it only doesn't work with armor. Like it says in the comments you can breed two horses with saddles only although I recall not being able to it doesn't matter because it seems to work now.
Linked issues
is duplicated by 6
MC-13796
Unable to breed horses
Resolved
MC-13967
Can't Breed some horses but it seems to be random but armour increases the chances of them not breeding
Resolved
MC-14182
cant breed horses
Resolved
MC-15442
Horse Armor Prevents Breeding
Resolved
MC-15963
Horse mating while wearing armor
Resolved
Attachments
Comments 5
Confirmed, but only with horse armor.
If one of them wears an armor, breeding fails.
Two horses wearing saddles can breed.
Jens Bergensten
I think it might be intentional