So is Jon Snow supposed to really forget about Bran and Rickon?

[Lord Lannister]

For those who know how a Dance with Dragons ends for Jon... his knowledge of Bran and Rickon being alive could conceivably cause Jon to keep sending repeated search parties north of the wall, despite casualties. Which would provide an alternate route for things to turn out the way the did in the book.

Though I'm sure D&D didn't think that plot thread through.

[AryaNymeriaVisenya]

When did Littlefinger tell Sansa that Arya was alive in Season 3?

Episode 1, on the watefront when Ros warned Shae about Littlefinger

[juniperstone]

Jon is a sworn brother, they give up their names, families. To put his vows, his honor, and the good of the realm above all else and swallow personal turmoil seems to be a Starkish quality.

[Masha]

For those who know how a Dance with Dragons ends for Jon... his knowledge of Bran and Rickon being alive could conceivably cause Jon to keep sending repeated search parties north of the wall, despite casualties. Which would provide an alternate route for things to turn out the way the did in the book.

Though I'm sure D&D didn't think that plot thread through.

Not really, he cannot ask his people to go on a suicide run (at this point in time) to find Bran. He is not an absolute ruler who can forsake his vows and sacrifice his people on a slim chance of saving his brother. Hardshome is hundreds/thousands of people - well worth the risk, 4 lonely people going north, not so much.

However, D&D should have had him mentioning Bran and others once a while if only to Sam for continuity sake. Otherwise, its another lost thread.