we know Ned has been set against Robert killing all the Targaryen offspring, so it would be natural that he may claim Rhaegar and Lyanna's bastard as his own to stop the child being murdered by Robert. Jon Snow's resemblance to Ned and "Northern" looks are emphasised early on, as he and Arya are the only children who look like true Starks. Ned's other kids look more Tully than Stark. Barriston Selmy alludes to it all, however, and also gives support to the idea that on Snow is the bastard of Ashara Dayne and Ned.