His character would likely be more hardened. Growing up in clan wars means facing danger and betrayal often. He'd be less trusting at first. For example, he might not be as quick to befriend Sasuke as in the original. He'd have a 'survival first' mindset.
The clan wars could also make Naruto more empathetic towards the underdogs. If he sees clans being oppressed or wiped out, it could fuel his desire to bring peace. However, he might also be more vengeful towards those who start or perpetuate the clan wars, adding a new layer of complexity to his character.
Naruto could develop a more strategic side to his character. Since clan wars involve a lot of planning and counter - planning, he'd have to think on his feet more. He might also be more aware of the importance of alliances and how to use them to his advantage. This would be different from the rather impulsive Naruto in the original story who often acts on his emotions.