I think the show writers have made it pretty clear in the 'Behind the Episode' videos that Sansa simply doesn't trust Jon yet.
Jon was the bastard of the family.
Although it's the only family she's got, they were never close to each other.
From Sansa's point of view, she does not know how Jon would react to news of Littlefinger coming.
She cannot trust him to make what she deems to be the 'right' decision.
While we all know how awesome Jon Snow is, Sansa doesn't.
She knows he's family (if a bastard) and that he was Lord Commander of the Night's Watch, but she was never close to him at Winterfell and never saw his exploits at the wall.
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Sansa held the reinforcements from Jon to ensure the numbers would be in her favour.
She knows Ramsay and the games he plays.
She knows (speculatively) that he will have total disregard for the lives of his men if it means he wins.
We see this play out, with archers raining arrows onto friend and foe.
In short: Sansa needs Jon to commit to the fight to ensure that Ramsay gets bloodthirsty.
If Jon knows about the reinforcements, he will not sacrifice free folk.
Sansa is becoming a shrewd leader.
Her time with Ramsay has made her pragmatic and unlike Jon and Ramsay
she is able to separate her emotions from the goal.
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Remember the conversation between Sansa and Jon before the war.
She was asking jon if he won't ask for her advice as she knows Ramsay bolton far close then anyone?
Sansa might have told jon if he had shown interest(or believed) in taking her advice.
As in their conversation Sansa says: If you had asked for my advice earlier, I would have told you not to attack Winterfell until we had larger force or is that obvious,too?
And Jon replies: When will we have a larger force?
We've pleaded with every house that'll have us.
The Blackfish can't help us.
We're lucky to have this many men.
As she was knowing the army they had won't be enough and Jon won't take support from Petyr Baelish as he made Sansa marry Ramsay.
This is seeming most obvious reason to me why Sansa won't let Jon know about it.
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I think that there are a few reasons for this: Little Finger cannot be trusted.
Ned learnt this the hard way.
He only does what he does so that he can benefit in some way.
Because of (1), and I may be under correction here, he doesn't want the help of Little Finger and he tells her this.
But she can see that Jon will need the extra men
so she does it behind her back.
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It's a better story.
It conforms to the way things happen in Game of Thrones.
It conforms to the characters.
It was in the end, the better strategy.
Bolton's were defeated because they came to the battlefield instead of withstanding a siege.
They came to the battlefield because Ramsay Bolton 'knew' that his army will defeat Jon Snow's.
They were beaten because they were taken by surprise when Baelish arrived.
As to why Sansa didn't tell Jon, it was simply because of the way she is, this is the kind of person she has become.
After years in king's landing, and everything she has undergone with her marriages with Tyrion (yes it was horrible for her) and Ramsay, one thing she has learnt is that she won't under any circumstances let anyone else control her life anymore.
"I'm not going there back alive." .
She won't tell anyone anything unless it serves a purpose for her.
Sansa is no longer the naive girl who wanted to be a queen and to have little price and pricesses.
She has seen it all, been through it all.
She is a survivor.
She knew that Jon won't be able to beat Ramsay.
Jon fights with honor.
"Ramsay is the one who lays traps." .
She also knew that to beat someone like him, she needs someone like Peter.
She wants Ramsay dead and she is willing to use Jon's entire army as bait to draw him out.
"Sleep well" , she says after telling Ramsay he is going to die the next day.
She also knows her brother is not going to survive this battle and accepts it with steely pragmatism.
Sansa has in fact become, a lot like Peter Baelish.
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Another point of view: What's in it for Little Finger?
Little Finger won't come to her aid if there's nothing in it for him.
In her secret letter, Sansa could have promised him the tittle of Lord of Winterfell, bonded by marriage.
Jon Snow won't let that happen.
Sansa is one of the few remaining and legitimate heir of Winterfell, and she knows she can't get there without Little Finger's military backing.
This is her best move, lets not let Jon get in the way.
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I think, Sansa want to be "the savior" in a war, to gain respect and then to smooth her path to be the queen of winterfell.
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My take is that she is somewhat embarrassed about her relationship with Baelish.
He betrayed her (and
Jon's) father, got her involved as a suspect in Joffrey's killing, killed his "wife" for her, overtly declaring his creepy you-look-so-much-like-your-mother love, and then sold her off to a torture-y demon of a man.
I am eager to see how him and Jon will get along, but I suspect he would not be as happy to see him as the occassion would suggest.
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Sansa Stark writes that secret letter to Petyr Baelish in  Season 6 Episode 7 of Game of Thrones, 'Broken Man'.   Why does Sansa Stark not want Jon Snow to know about getting help from the Vale during their conversation in Episode 9, 'Battle of the Bastards?'
Why does Sansa Stark not want Jon Snow to know that she had written a secret letter?
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I think the show writers have made it pretty clear in the 'Behind the Episode' videos that Sansa simply doesn't trust Jon yet.  Jon was the bastard of the family. Although it's the only family she's got, they were never close to each other. From Sansa's point of view, she does not know how Jon would react to news of Littlefinger coming. She cannot trust him to make what she deems to be the 'right' decision. She knows he's family (if a bastard) and that he was Lord Commander of the Night's Watch, but she was never close to him at Winterfell and never saw his exploits at the wall. Moreover, Little Finger won't come to her aid if there is nothing in it for him. Jon won't let her marry Little Finger if that is what she is planning. Sansa cannot trust him to make what she deems to be the 'right' decision
Sansa and Jon Snow were never close to each other. She does not know how Jon would react to news of Littlefinger coming. She cannot trust him to make what she deems to be the 'right' decision. Sansa knows he's family (if a bastard) and that he was Lord Commander of the Night's Watch, but she was never close. Sansa could have promised Little Finger the tittle of Lord of Winterfell, bonded by marriage. Jon Snow won't let that happen. Sansa knows she can't get there without Little Finger's military backing. This is her best move, lets not let Jon get in the way.