Nah
Let's play say no one played into anyone's "trap." Say Jon turns around, gets Ramsay to charge into his army like he had planned.....the result of the battle would have still been enormous losses on Jon's side....and then he'd STILL have to chase Ramsay to Winterfell with a depleted army (if there would be any army at all) where they'd continue to get picked off and killed by the archers. Without the additional men, Jon was going to lose......he only compounded that problem by charging first and falling into Ramsay's trap. Sansa didn't play into anyone's trap...her hand was forced by the dire situation unfolding in front of her. Of course, she could've still chosen to not send out for him....but seeing how everything played out, we know that would've been the end of Stark-set outside of Bran and Arya
Sansa played into littlefingers trap by not trusting Jon.
Jon played into Ramsey's trap but it was understandable. He literally saw his little brother run for his life and then get killed in front of him. That's pretty hard to just dismiss and get ready for a battle.