Jon's strategy made no sense. Jon's army HAD to attack, since they are the ones that want Winterfell. All Ramsey had to do was wait. They even had the burning effigies lined up to give his archers range markers for more accuracy. Ramsey had the perfect upper hand in a defensive battle (Higher ground, 2x troops size). I don't think Jon executing on his strategy would've mattered at all.
Not that it matters, but Jon's strategy did make sense. They were going to attack, but not Jon going full ham alone. Forcing his cavalry to charge full tilt to save him. After attacking with the strategy they were originally planning, they were anticipating Ramsey's men would push forward if the center of the Stark forces gave. Drawing them into the defensive positions Jon's army had prepared. The whole point was to prevent that shield wall envelopment maneuver they were caught in, due to Jon getting played by Ramsey.
We were laughing when it was explained to Giantsbane. His face was hilarious when they were using words like envelopment and pincher.
It could have worked to. Ramsey would have no control over the men that are in the middle of the fight. If those men press an advantage in the heat of battle. Instead of disengaging and falling back to original positions, they end up where Jon expected them to.
Another indication that Jon was right about Ramsey's overconfidence? Ramsey even fighting him in open battle. Jon did not have seige equipment or provisions to sustain one. No logistical lines of supply; nothing. Ramsey could have stayed in Winterfell. Precisely as he was going to attempt, after losing the battle. Right up until the wun wun gate crashed him. Which he could not have done if Ramsey had all his archers. They would have pin cushioned him before he could near the gate.
But it WAS a desperate move, and Jon WAS a dumb ass. He was trying to save his bro, which was not going to happen. Should have been more patient and listened to his sis. Her emphatic point was "Don't do what he wants you to!" and he still did. Jon Snow knows nothing.