Naruto could become cold due to disappointment. He might have expected Sasuke to rule in a certain way, but when Sasuke becomes Hokage and starts making decisions that seem contrary to Naruto's ideals, Naruto feels let down. This disappointment could turn him cold towards Sasuke and the village in general.
Their relationship could become more of a partnership. With Naruto as Hokage, Sasuke might be more willing to work within the village's framework. They would still have their friendly rivalry, but it would be more focused on making the village better.
They still have that deep friendship, but it's more official. Naruto as Hokage respects Sasuke's views on matters related to the outside threats. Sasuke, on the other hand, respects Naruto's leadership. They often meet to discuss strategies and how to keep Konoha and the ninja world in peace. For example, they might plan together how to deal with any potential threats from rogue ninjas or other villages.
One possibility is that Naruto might feel a sense of isolation. Since Sasuke has achieved the highest position in the village, Naruto might feel like his own journey and achievements are overshadowed. He could become cold as he withdraws into himself, thinking that he no longer has a clear purpose in the village where his best friend now holds all the power.
Well, usually it starts with Sasuke realizing his newfound leadership role. He might struggle at first with the political side of being Hokage, which is very different from his combat skills. Naruto would be there to support him, of course. And then they would face some new threats to the village together. The story could also explore how Sasuke changes the way the village is run, maybe bringing in some new ninja training methods inspired by his own experiences.
Naruto could change Konoha by promoting unity. He might organize village - wide events where everyone, from the strongest jounin to the youngest genin, participates. This would strengthen the bonds between the villagers.
The dynamic would shift a bit. Naruto would have to balance his friendship with Sasuke and his duties as Hokage. He would probably try to bring Sasuke more into the fold of the village, making him feel like a true part of it. Sasuke, in turn, would start to see the village in a new light, through Naruto's leadership. Their relationship would be a key factor in the stability and growth of the village.
Naruto's personality might become more reserved in some ways. As Hokage, he has to represent the village in a more solemn and diplomatic manner. He can't be as carefree as he used to be. For example, in international meetings, he has to think carefully about his words and actions.
Naruto's family would become a symbol of the village. His wife and children would be in the public eye more often. This could mean added security concerns for them. At the same time, Naruto would try to instill in his family the values he wants to see in the village, like hard work and loyalty.
In many time travel fanfictions, their relationship often becomes more understanding. Since they already know each other well in the future, when they travel back, they can skip the initial hostilities. For example, if they go back to their academy days, Sasuke might not be as cold to Naruto as he was originally because he already knows Naruto's true nature and what they will go through together in the future.
Well, Naruto's newfound maturity might lead to a more understanding relationship with Sasuke. He could approach Sasuke with more wisdom and less impulsiveness. Maybe he'd be able to better see Sasuke's pain and reasons for his actions, and Sasuke might start to respect Naruto's growth more, leading to a less adversarial and more collaborative relationship between them.