There are some people that think that it won’t be important but listening to the quotes HBO decided to use for this teaser it’s clear that the revelation will play a big role in the next season because it’s something that had deep consequences in their family from the beginning ( Ned’s promise to Lyanna had a significant impact on how Catelyn saw Jon but Ned protected Jon anyway because he is a Stark, not in name but by blood).
That said the new Stark generation is united and will move on from the past years of misunderstanding and secrets ( see how Jon and Sansa looked at Ned and Catelyn statues but they moved forward without stopping) and I think the final moment of the teaser means that they will stand together against the coming storm.
Last season, when they were in the crypt, Littefinger said to Jon:
Your father and brothers are gone, yet here you stand King in the North.
Last best hope against the coming storm.
and in the new teaser of season 8 we saw that now the coming storm is literally at their heels.
Maybe, but there is the fact that in season 7 Littlefinger words suggested that Jon will face the coming storm alone while the teaser suggested that Jon, Sansa and Arya will face the storm together and we all know that “the lone wolf dies but the pack survives”.
It's Lyanna's ostrich feather, freezing. The Others are coming, bringing the cold. Lyanna’s statue holds a feather in her hand. It is akin to the concept of Maat and Thoth. The ceremony of weighing the heart against a feather.
In ancient Egypt, Maat, a creation goddess wears an ostrich feather upon the crown of her head, representing the heart. The heart is the place inside of us wherein they believed the soul resides. Lyanna's statue, as well as Maat, both stand on a flat, solid base representative of harmony, balance and order. The balance of the world. Maat also represents the stars and seasons, and the effect that the actions of men and gods have on this world. It is the action of doing right by one another and nature, living in harmony with natural law and with others that the world remains in chaos after creation or in order, based on their actions. Maat and her counterpart, Thoth, or Hermes, work together with the Anubis, who is depicted as having the head of a dog (or wolf), just as the direwolves lay at the feet of the Kings of Winter. Together, they weigh the heart against a feather to ensure the soul has the lightness to take the journey to the stars from the Duat, or the Underworld. The Others represent the Underworld or Otherworld, the land of the dead.
In our story, the actions of men and gods decide the fate of the world, the seasons and the soul. Lyanna and the Kings of Winter in the Crypts of Winterfell seem to be representing this ceremony. Now, Jon, Arya and Sansa as well. Her feather is lying on the ground, freezing.