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.
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.