One interesting 'Adventure Time Ice Queen' fanfic could be about her backstory before she became the Ice Queen. It might explore how she got her powers and what led her to be so cold - hearted.
One popular plotline is the Ice Queen's journey to find true friendship. In many fanfictions, she starts off as a lonely and misunderstood character. Another plotline could be her attempts to gain more power in the Land of Ooo, which often leads to conflicts with other characters like Finn and Jake. Some fanfictions also explore her past and how she became the Ice Queen in the first place.
Power and its consequences is also a frequent theme. The Ice Queen has powerful ice - based abilities. Fanfictions might delve into how she uses or misuses her powers, and how it affects her relationships with others in the Land of Ooo. Some fanfictions also focus on her backstory, trying to explain how she became the way she is, which could involve themes of loneliness and isolation as she is a rather solitary character in the show.
The Ice Princess stood in her glacial domain, her icy hair flowing like a frozen waterfall. She was lonely, as always. One day, Finn and Jake came by on an adventure. They were initially cautious, but Finn's kind heart reached out to her. Jake, with his goofy charm, made her laugh for the first time in ages. They decided to have a snowball fight, and the Ice Princess found herself truly enjoying the company. This simple encounter changed her view of the outside world.
Archive of Our Own (AO3) is also a great place to find 'Adventure Time Ice Queen' fanfics. The tagging system there is very useful. You can search for tags like 'Ice Queen', 'Adventure Time', and also filter by things like rating, word count, and genre to find the perfect fanfic for you.
Marceline is a very common side character in Ice Queen Adventure Time fanfiction. Their personalities are so different that it creates interesting interactions. Another common one is Princess Bubblegum. Since the Ice Queen often has conflicts with the Candy Kingdom, Princess Bubblegum is bound to be involved. Also, Peppermint Butler sometimes shows up as he is often associated with Princess Bubblegum's court and can add an element of mystery to the story.
The unique element is often the exploration of Finn's different personality in his ice form. He can be more cold - hearted in a literal sense, which creates interesting conflicts.
One common theme is redemption. Many fanfics explore the Ice King's past misdeeds and his attempts to make up for them. For example, he might try to apologize to Princess Bubblegum for all the times he kidnapped her.
A great plot for an Ice Princess fanfic could be that she falls in love with a new character, a fire elemental. This creates a conflict as their elements are opposites. The Ice Princess has to decide whether to follow her heart or stay true to her icy nature. Meanwhile, the other characters in Adventure Time like Marceline and Lumpy Space Princess get involved, trying to give her advice on love and identity.
You can try fanfiction websites like Archive of Our Own (AO3). It has a large collection of Adventure Time fanfictions, including those about the Ice Queen. Just search for 'Adventure Time Ice Queen' in the search bar, and you'll get a list of relevant stories.