All Sansa did was run and call for help after she got pissed after seeing Ramsey again the day before the battle. Little Finger offered to bring the Vale to help retake Winterfell at that meeting in Moles town and she was still in her feelings and threatened to kill him instead. Jon kept saying they needed more men and she still refused to use the Vale's army.
When Jon got tired of begging smaller houses for help he said fukk it lets go with the army we have she was still trying to round up northern houses that barely had soldiers at all . It wasn't til she got into her feelings at the pre battle meeting that she swallowed her pride a d ran and got Little finger to provide the help she had previously turned down. See the vid velow around the 3:40 mark shen she herself says they dont have enough men and still never mentions the Vale army that had been offered to her that Jon never knew about.
I personally hold her responsible for losing so many wildlings and the last giant among them.
That is all her fault. Had she let it be known that the Vale army was available to help Jon wouldnt have lost half his forces at the battle of the b*stards. If i was Thormund and i find that out i'd be pissed.
So all the sudden she's a boss talking about "we have Winterfell because of me"? (See 0:45 mark below)
Doggy, LittleFinger is the real boss here. He made her what she is now. He just messed up and allowed his greed and love for her lead him into underestimating her, his own pupil, to his death. Plus he misjudged the bond between Arya and Sansa and admit it YOU DID TOO.
I'm still pissed at that red-headed little bratt and still wish she was dead in a way .

If it wasnt for her we'd still have over 2000 wildlings (fighting men) and a giand instead of the few we have now. Arya and her mom were the true Gs among the women in Winterfell.
The show runners put all of this in the show in Season 6 for a reason breh. If they wanted Jon to win the Battle of the b*stards all on his own, they would've. Instead they showed pretty plainly and clearly that Jon would've lost. But anyway. Try to see it from Sansa's point of view for five seconds.
Littlefinger didn't control anything in the Vale. The Vale lords hated him or did you not get that when he got his throat slit. Here is a clip of him begging them to save him since you clearly forgot about all that
Sweetrobin controlled the Vale. Littlefinger manipulated Sweetrobin. And Sansa manipulated Littlefinger......THEREFORE????

Plus Sweetrobin would've did anything for Sansa anyway since she was his cousin. Here is that scene again for reference since yall forgot.
The Northern Lords were not taking Sansa's opinion into consideration even though she spent the most time with Ramsey. She mentioned that multiple times. She wasn't being consulted with and they were acting like she was intruding when she came around. And it probably bothered her that everyone went automatically to Jon as the leader, as if she wasn't important enough because she was a girl.
Plus, she was hearing their gameplan. It was weak. Jon wasn't taking Ramsey serious. Again, the show runners put that in there for a reason
("I fought the Whitewalkers, I fought Thenns, I been behind the wall yada yada yada, I'm not scared of Ramsey"). And what happened....Ramsey did EXACTLY what Sansa said he was going to do. He baited Jon until he lost his cool. Jon could've won that battle. 2,000 men vs. 6,000 men isn't impossible odds.
There were so many wars throughout real history where people with worse odds won. But he rushed into battle recklessly and before long Ramsey had his army flanked and surrounded.
Sansa said she wasn't going back to Ramsey alive. Sansa didn't trust that Jon and the Northern lords would beat Ramsey based on the points said above. Sansa knew that Ramsey was smarter than all of them. And as much as I love him, Jon did not disprove that on the battlefield. Letting your army get surrounded is war 101 on what
NOT to do breh

So Sansa kept the Vale in her pocket and like she thought he would, Ramsey walked right into the trap. How yall twist that into Sansa
NOT beating Ramsey at his own game is a mystery to me. What other female character not named Dany was strategizing secret war plans? Let us know.
And to your last point....soldiers were going to die regardless. Had Sansa told Jon about the Vale there's the very real possibility that Jon would've still lost the war with extra men

because Ramsey would've still baited him on the battlefield. This would've caused countless casualties to the Vale. Sansa's method kept the entire Vale army intact. Another alternative is Ramsey might not have met them on open field. He might have went back to Winterfell and made it a siege. Wun Wun would have still died charging through the gate. The only difference is instead of sieging the castle against a handful of soldiers left to defend Ramsey, Ramsey would have had 6,000 men in there. And knowing how sick Ramsey was in the head, he would have done something to trap them. Maybe Ramsey would've told his men to focus majority of their arrows on Jon. There's no guarantee they would've won that way either. It worked out the way it worked out because the showrunners wanted it that way and Ramsey had to be caught off guard to be beaten.