Actually the simplest explanation to why Obito has horns, is that Jyubi itself had horns and Jinchuriki tend to gain the Bijuu's characteristics when utilizing their power (also let's not forget that Obito is the only shown Jinchuriki that had sealed a Bijuu's real actual body in himself and not only chakra, while in Kurama's flashback of So6p, Sage already had only the bijuu's chakra in him, thus he could be looking differently than when he had the whole Jyubi in himself).

The reason why Minato and Naruto look like that is because they are the only ones that use that kind of seal, which basing on what Kurama said, it is the sealing jutsu that So6p himself used.