Should it be Jon? Yes! But, Littlefinger is in a far better position to claim the lordship of Winterfell because 1) he has the might - he has the Knights of the Vale with him and basically controls the young Lord of the Vale; 2) he has the official political position, since he has already cut a side deal with Cersei, who still has some influence with King Tommen, who can issue an official decree; and 3) Sansa owes him big-time for bringing the Vale knights, so if she agrees to marry him, then he has a legitimate Stark in his family.
The only way Little Finger holds Winterfell is by force. The northern lords have defeated the Vale many times in the past and won't let a vale leader rule the North. They give two shits about an order from King Tommen. Just a prediction that they will name Jon the King.
I have some other predictions, but I don't wanna ruin it for anyone. Some big names dying tomorrow.