There may be something to Sansa not caring about or perhaps even wanting the death of as many of Jon's men as possible. Remember how she continues repeating some variation of "no one can protect me", so she's probably thinking the only way she can be safe is by being in a position of power herself. That's not the sister of a Lord or one's niece, she wants her own lands and armies loyal to her. However, I believe the main reason she didn't tell Jon is because she simply didn't know if Littlefinger's army would show up on time, or at all. There's really nothing different Jon could have done, other than perhaps be a bit more conservative, but it's not like Sansa didn't warn him not to charge in like an idiot.