After the "Battle of the Bastards", Game of Thrones fans began to hail Sansa Queen of the North and with good reason. The only reason Jon Snow was able to defeat Ramsay Bolton was because Sansa sent a letter to Littlefinger and he, along with the Knights of the Vale, came to the rescue. If it hadn't been for Sansa, Jon Snow would've lost and most likely died and one only knows what could've happened to Sansa. It's clear that Sansa knows what it takes to be a good leader, and that's just one of the many clues that Sansa will probably rule Winterfell.
Sansa has been through a lot. From the time she left Westeros, she had to watch her father be beheaded in King's Landing, stay there and play nice with her enemies, get married off to Tyrion and then later Ramsay, where she was raped and abused by him. The list goes on and on. But through all those terrible experiences, Sansa has learned a lot and now, although she still holds a lot of the qualities of a Stark, she's also more ruthless and empowered. Sansa's ready to do whatever it takes to get what she wants and to make sure no one has power over her ever again. There's no doubt that she's ready to rule Winterfell.
She Knows How To Play The Political Games
Sansa has lived with her enemies and she knows how to stay alive. One of the biggest issues of the Stark men is they were led by honor, which is great, but is also what led to their deaths. For example, unlike her father, Sansa would've known to not tell Cersei that she knew about her children not really being Baratheons. There's a lot that comes with being a good leader and sometimes a part of that is choosing your battles wisely and Sansa knows how to do that.
Although some people didn't like or understand how Sansa could be so accepting of Rickon's fate, the truth is she was being realistic. She knows Ramsay better than anyone and she knew when a battle was lost. She also knew that Ramsay would try to trick Jon, so she warned Jon to go into the battle with a clear head (but of course he didn't listen).
She Has Powerful Allies
Whether you trust Littlefinger or not, he did prove he's got Sansa's back. Having the Knights of the Vale in her pocket is very helpful, and she'll probably need them again to keep Winterfell protected. Additionally, although Sansa hasn't seen Margarey in a while, they did establish a friendship. Margarey also knows how to play the game, so she won't align herself with Sansa unless it benefits her, but Sansa could have a great ally in Margarey, as well.
She's A Stark
This may seem obvious, but the truth is Jon Snow isn't a Stark and he, therefore, isn't a legitimate heir. We all love Jon Snow (and most of us believe he's a Targaryen at this point, anyway) but he technically doesn't have a claim to Winterfell. And since Bran is still north of the Wall and Arya just left Braavos, the only one that has a rightful claim to Winterfell currently is Sansa. Plus, truthfully she deserves to lead her home. She's worked hard for it and they wouldn't have it back if it wasn't for her. All hail Queen Sansa!