Finn has been shown a few times throughout the series' run to be able to have prophetic dreams (dreams that involve the Cosmic Owl in some way). However, the one that has the greatest significance is the one that occurs in "Frost & Fire", yet I find it difficult to believe that the Cosmic Owl is merely phophesying Finn and Flame Princess's breakup.
So then, what was the Cosmic Owl really trying to tell Finn?
In my view, I believe that the Cosmic Owl was foretelling something much more significant, as evidenced by the chain of events listed below, that take place after Finn's dream in "Frost & Fire".
This is merely speculation as of now, but all of the events listed take place in the show's canon by broadcast, not by production order.
Events (as of "Ocarina")
"Earth & Water": Following the events of "Frost & Fire", Ice King moves into Finn and Jake's Tree Fort, due to the fact that the Ice Kingdom was destroyed by Flame Princess, leaving him homeless. In addition, Flame Princess and Cinnamon Bun stage a coup against the Flame King and seize control of the Fire Kingdom.
"Play Date": Since he began living at the Tree Fort, Ice King does nothing but bother Finn and Jake, so they invite Abracadaniel over to play with him and get him out of their hair. This eventually leads to Finn breaking Joshua's Demon Blood Sword in exchange for their freedom at the hands of Kee-Oth the demon.
"Blade of Grass": Since Finn's Demon Blood Sword is broken, he is in need of a new one. He aquires the cursed Grass Sword from the Grassy Wizard, which binds itself to his body, and sometimes seems to control his actions. The Grassy Wizard tells him that it is an "eternal curse", and that the sword will be a part of Finn for eternity. Finn also has another premonition dream in this episode, which foretells the events of "Escape From the Citadel". However, this dream does not involve the Cosmic Owl.
"Billy's Bucket List": While trying to finish Billy's bucket list, the last entry is "Lie on my back in the ocean. Just float.", which Finn cannot do, due to his intense thalassophobia. However, the Grass Sword slices through the Fear Feaster living in Finn's stomach, allowing him to float in the ocean, finish the bucket list, and communicate with Billy, who tells him that his father, Martin, is imprisoned in the Citadel.
"Escape From the Citadel": Finn and Jake manage to get to the Citadel by following the Lich, who committed a cosmic crime by murdering Prismo in the previous episode. Once there, the Lich unleashes a fiery plague that frees all of the imprisoned Cosmic Criminals and kills all of the Citadel Guardians. The Lich is turned into a large humanoid baby by the Guardian's blood, and Finn's father, Martin, escapes with the other criminals into space. Finn tries to stop them, and ultimately, his right arm is torn off by the Grass Sword, and a flower grows in its place after his stump is touched by Guardian blood. The baby-fied Lich is abandoned with Tree Trunks and Mr. Pig.
"Breezy": After falling into a deep depression, Finn regains his right arm when the flower that grew out of his stump blooms into a tree, and reveals an arm covered in honey inside. However, there is a large green thorn growing out of Finn's palm. The exact nature of this thorn is, as of now, unknown, though it could be a continuation of the eternal curse placed on him in "Blade of Grass".
- That is all of the events as of now, but they all happened due to Finn's actions in "Frost & Fire", which were seemingly prophesied. I will add more to this collection of data as more is revealed.
Thanks for reading!