Sakura could become determined to find out the reason for Naruto's coldness. She may try to get closer to him to figure it out, despite his cold attitude. For instance, she might keep inviting him to do things together or try to start conversations with him.
She might be confused at first. Sakura is used to Naruto being friendly and now his coldness would be a big change. She may start to question what she did wrong.
One possible reason could be that Naruto has his own unrequited love for someone else and he is trying to distance himself from Sakura to avoid leading her on. For example, if he has deep feelings for Hinata, he might be cold towards Sakura to make his own feelings clear.
One reason could be that Naruto is focused on his own goals like becoming Hokage and he might see Sakura's feelings or her actions as distractions. He has a lot on his plate and may not have the time or energy to deal with her in a warm way.
Sakura might initially be confused. She has known Naruto for a long time and his sudden coldness would be unexpected. She may try to reach out to him to find out what's wrong.
She might be confused at first. Sakura is used to Naruto being friendly and always there for her, so his coldness would be unexpected. She may start to question what she has done wrong.
Sakura might be completely shocked at first. She might freeze for a moment, not believing what's happening. Then she could start crying tears of joy and say yes immediately.
She might be heartbroken. Sakura could initially be in shock and then fall into a deep sadness. She may blame herself for Naruto's leaving, thinking that she could have done something differently.
At first, Naruto might be really confused. He's used to the normal Sakura, so when she starts acting all yandere, he'd be like 'What's going on, Sakura - chan?'. He'd probably try to talk to her and find out what's wrong.
Well, in some fanfics, Naruko's coldness towards Sakura could be a result of a past event. Perhaps Sakura made a mistake that affected Naruko or someone Naruko loves. Another aspect could be the power dynamic. If Naruko is more powerful or has a special ability that Sakura doesn't, and Sakura shows envy or something similar, Naruko might react with coldness.
One possible fanfic could be that Sakura has resentment towards Naruto because she feels he doesn't understand her true feelings for Sasuke. But then, during a dangerous mission, Naruto saves her life in a heroic way. This act makes Sakura realize how much Naruto truly cares for her. In a moment of emotional turmoil, she impulsively kisses him, which then leads to a series of events where they have to confront their feelings for each other and also deal with the implications within their team.
She could be heartbroken. Sakura has always loved Sasuke deeply, so his leaving for Naruto would be a huge blow to her. She might initially be in denial, not believing that Sasuke would choose Naruto over her.