Personally I think the wildling woman took Rickon off into the wilderness to await the results of all these wars. If the Starks or their allies return to power she can find great favor by producing Rickon, and if they don't, well, she can garner favor with whoever does.
Legality aside, since the current Westerosi circumstances aren't that conducive to lawfulness and exactness and such, the identity of Robb's heir is really a moot point, since Winterfell will belong to whichever Stark can rebuild and hold it. I don't see them fighting over a castle among themselves after all the sh*t they've been through. If indeed they do reclaim it. In my opinion the most likely to rebuild or reclaim Winterfell are Sansa and Bran. Sansa because I foresee her becoming a great Lady with her impending marriage and the will to do so. I think her snow castle in the Eyre was foreshadowing. Bran because, although IMO more unlikely, his namesake was a legendary builder. Weak reasoning, I know, but GRRM has a habit of things like that turning out to mean something.
I sincerely doubt Jon will ever be more than Lord Commander. I don't think he wants, or will want, to ever be more than that.
Arya is not interested in politics or settling down. At least not at this juncture, things could change.