First off, I know I am late to this. Now, since last year, there was rumour of an ornithischian from Siberia with feathers. It was called "Kulindodromeus". Well, it is finally described, but is called "Kulindadromeus". This has got to be the coolest thing going on here. As an ornithschian with feathers, this little herbivore has provided the best evidence that all dinosaurs had some sort of feathering. What is more, is that the earliest dinosaurs had feathers. Ornithischians and saurischians evolved not long after the first dinosaurs appeared. So feathers probably evolved before that split occured.
You also have pycnofibers on pterosaurs, and the ancestors pterosaurs split off before the first ancestors of dinosaurs appeared. Feather like filaments probably evolved in the early Triassic, before that pterosaur/dinosaur split occured. However, before we say that this is absolutely true, we have to do some sort of skeptical work. Some people have suggested that feather like structures evolved several times in the dinosaur line. However, I don't think so. I think that these feather-like filaments on Kulindadromeus are homologous with those on theropod dinosaurs. While we have the best evidence of an entire line of feathered animals to date, the final proof would probably be a very early dinosaur with feathers.
This also had me think about feathered sauropods. Before this, I never really thought sauropods were feathered. But, it had me thinking. Sauropods are saurischians, and the majority of feathered dinosaurs are saurischians. My very speculative theory, is that when born, young sauropodlets possessed downy feathers, like those of a newborn chick. However, overtime, I think that the young gradually lost the majority of feathers, with only their feet having feathers when fully grown. I have no proof of this, but it is entirely possible. Also, this is further proof of endothermy in dinosaurs (not that it needed much more proof), and that endothermy goes even further back on the archosaur line than thought. Also, crocodiles have dormant feather producing genes, and this seems to support that too.