Well, it might be that in the fanfiction, Naruto goes to the frozen waterfall to have a conversation with Kyuubi. They could be discussing Naruto's growth as a ninja and how Kyuubi's power can be better harnessed. The frozen waterfall setting adds a sense of isolation and mystery to the encounter.
Another possibility is Gaara before he met Naruto. He had a really tough childhood and was initially very cold - hearted, seeing others as tools or threats. His heart was like a frozen desert, until Naruto's friendship started to thaw it. In this fanfiction, they could explore more of his pre - Naruto state of a frozen heart and how it affected his relationships with others in the shinobi world.
In Naruto fanfiction, an emotionless frozen Naruto can be a really interesting concept. It might be due to some dark magic or a traumatic event. This could lead to a very different story line, like his friends trying to bring back his emotions. Maybe he was frozen in time and lost his ability to feel during that process.
One common theme is the struggle of the frozen fox to fit in. Since it's a unique creature in the Naruto universe, it often has to deal with being different from the regular ninjas and villagers.
Well, it could be about a character in the Naruto universe who has a frozen heart, perhaps metaphorically. Maybe it's a ninja who has been through so much pain and loss that they've become cold and unfeeling. And the story could be about their journey to thaw that frozen heart, maybe through the friendship of Naruto and his gang.
Naruto and Hinata are common characters. Their relationship can be given a 'frozen' twist in fanfiction. Maybe Naruto is too focused on his goals at first and seems cold towards Hinata's feelings, creating a sort of frozen state in their relationship that needs to be thawed. Sasuke can also be a character in these. His brooding nature can be seen as cold, and his potential romantic relationships, whether with Sakura or someone else, can be explored in the context of 'frozen romance' as there are often barriers and coldness between them due to his past and his personality.
It's hard to say for sure without reading it, but it could be Naruto himself. Since it's a Naruto - related fanfiction, he might be the central figure dealing with the frozen flame concept.
Another popular theme is friendship. Naruto is known for his ability to make friends. In Naruto Frozen fanfiction, he might form strong bonds with the likes of Anna, Elsa, and Kristoff. These friendships could lead to new adventures and help in solving the problems that arise in the combined Naruto - Frozen universe.
One way to portray an emotionless frozen Naruto in fanfiction is through his actions. He might stop using his usual energetic jutsu and instead rely on cold, calculated moves. His speech could also be monotone, lacking the usual passion. Like when he talks to his friends, there's no warmth in his voice.
It could be a new ice - using ninja who has a grudge against Naruto. Maybe this ninja wants to prove himself as the most powerful ice user and sees Naruto as a threat, so he freezes Naruto in ice.