I feel like the start of winter is the start of the Starks rebuilding and making things right in their own way. They're the family that embraces winter and we're seeing some major developments with some of the children just as snow is starting to fall. By the time winter comes around, they'll be making moves and we'll see a resurgence in the Stark name I hope.
I just feel like the timing of some of the snow flurries are meant as symbolism as well. Sansa in Winterfell as she goes through more shit but is finally reaching the turning point I believe, Jon beyond the wall becoming a real leader (I swear Olly, if you harm him...) and beyond those scenes with snow in them, we know Arya is progressing in her storyline, Bran seemingly has a big role in the supernatural aspect of the show which we'll hopefully see next year, and Rickon is doing Rickon things somewhere but it doesn't matter because I'm sure he'll someday lead House Stark.
Edit: Oh, and Benjen Stark is probably chilling with the white walkers having a good time.
Their motto of "Winter is coming" is fitting beyond the obvious reasons.
I just feel like the timing of some of the snow flurries are meant as symbolism as well. Sansa in Winterfell as she goes through more shit but is finally reaching the turning point I believe, Jon beyond the wall becoming a real leader (I swear Olly, if you harm him...) and beyond those scenes with snow in them, we know Arya is progressing in her storyline, Bran seemingly has a big role in the supernatural aspect of the show which we'll hopefully see next year, and Rickon is doing Rickon things somewhere but it doesn't matter because I'm sure he'll someday lead House Stark.
Edit: Oh, and Benjen Stark is probably chilling with the white walkers having a good time.
Their motto of "Winter is coming" is fitting beyond the obvious reasons.