I think Jon will ride a dragon, but I've always thought dragon riders are overrated. They are badass because they have a dragon. All they really do is sit on the back of a creature and give orders, while the dragon does all the work. It's kind of like horse racing- the riders get all the glory for training the horse, but it was really the horse that ran the race. With dragons, it is not an equal fight in most cases. The men fighting on the ground don't really stand a chance against flames reigning down on them. It is not even a fight.

I personally find the idea of Jon facing the army of the dead, wielding a sword (maybe Lightbringer) and giving men the courage to follow him into battle against monsters, allot more badass. There is more at stake. You have to face the enemy with nothing but bravery and a weapon in your hands. You have to face their blades and meet their eyes.

I think Jon riding a dragon for the most part of the Long Night, takes away from who his character has been built up to be in the show. He leads men against terrible odds, among the chaos where he has to physically and emotionally struggle. He never wields more power over his enemy making him superior (like riding a dragon), if he wins then it is down to his skill and luck. It feels more raw that way.