Sansa had the opportunity, straight out, when she asked Jon to wait and he said that they had no reason to as nobody else was coming.
Details didn't matter so much as waiting about 12 hours to coordinate the attacks.
You think she shut her mouth out of pettiness and shame of her relation with LF?
If that's true I chalk that under stupidity option.
http://www.vulture.com/2016
This article lists 5 options, none looking too good imo.
1 She thought Jon couldn't be trusted with the info. Basically she is calculating, withholding infos because she is either petty (getting back at Jon for not being involved in planning), or a pawn of LF in distrusting het brother. Thats a stupid option.
2 She used Jon and his men as unknowing bait, to get Ramsay out of Winterfell. Thay's one borderline evil option
3 Ashamed of her relation with LF and what happened. Why would that get in the way of telling Jon, I'm not sure. She could make up stories. That's the other stupid option.
4 She wanted any victory to be -her- victory, to solidify her claim. That's the other borderline evil option.
5 The writters wanted a Gandalf the White moment.
Option 5, sadly, is probably it, but we'll see what she has to tell to Jon.