The wagon will move.
The wagon moves because the force we exert is greater than the force of the wagon pulling back.
What pushes the wagon forward? It's the ground! The wagon pushes backward on the ground, so the ground pushes forward with an equal force. If the wagon can push back against the ground with a force greater than its resisting force, then the horse will accelerate.
What forces act on the wagon? The wagon pulls it forward, and there is a backward force from the ground: friction. If the wagon pull exceeds the friction, it will accelerate.
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