Even Summer, Bran's direwolf, who is an outstanding character in the series has the same coloring as the rest. I think that making Shaggydog special in coloring might imply something, the same way Ghost's color may imply something about Jon's origins and character. By that, I don't necessarily mean that Rickon will turn dark or wild but that he will have a distinguishing role to play. Otherwise I see no point in making him black and not grey as the rest.
I don't know if this is of any importance but I have been thinking about it a lot. It is common talk that Ghost's colouring has a deeper meaning. Why not be the same for Rickon's Shaggydog as well? I mean, I see everywhere written how Ghost is different from his brothers, but Shaggy is too, in a less obvious way. The rest of the direwolves have grey fur and yellow eyes whereas Shaggy has black fur and green eyes. I think Rickon will play an important role even in an inderict way due to his age but still he will have a contribution to the story. And maybe his direwolf's name implies this role, perhaps he will help reveal a "shaggydog story" that's been building up.