I'm choosing to view Sansa keeping the Vale army a secret from John as pure strategy. If John had known, he would have incorporated them in his battle plan and lost the element of surprise. I think Sanda knew that to beat Ramsay, she had to outsmart him and to do that she had to keep John in the dark. She needed John to behave as he would if he were fighting without reinforcements (which he did, since he didn't know there were any) to ensure Ramsay believed he had won before swooping in and taking him down. I don't think the secret was a lack of trust in John as a person, I think it was a necessity in order to outplay Ramsay.