Disclaimer: The Hunger Games trilogy belongs to Suzanne Collins, as do all of its characters, places, etc.
She is six years old when she dreams that President Snow is chasing her through an abandoned Capitol street as the buildings around them burn with a strange, shimmering, and oddly beautiful fire. His mouth is dripping with blood and flecks of it stain her white dress as he calls to her—"Euphemia! Little Effie!"
She wakes up trembling and bolts out of bed, running to her parents' room, not daring to look behind her for fear that Snow will be there.
She doesn't bother to try and wake her dad. Even at her young age, she understands that he is passed out cold from all the sleeping pills he's taken. Nine years in the future, when his only child is fifteen, he'll take too many of those pills. She'll come home from school, excited to tell him that she's finally managed a passing grade in her algebra class, only to find him sleeping in his armchair. When she tries to rouse him, she'll realize that he has gone to sleep forever. The doctor will rule it as an accidental overdose, a thing not uncommon in the Capitol, especially among the well-to-do who can afford the fancier drugs, but Effie will know better.
Her mother is annoyed at being awakened and refuses to comfort her child, simply telling Effie to go back to bed. Little Effie does so with tears in her eyes. Back in her room, she crawls underneath the covers, seeking shelter, convincing herself that nothing can hurt her as long as she's cocooned in her comforter. It turns out that she is correct—Snow does not come to swallow her up into his gaping, bleeding maw, and eventually she falls into a dreamless sleep.
In the morning, when she mentions the dream to her parents, her mother coldly tells her to forget about it and never to mention it again, not to anyone. Effie is hurt, but later in her life she'll remember the dream and understand her mother's reaction. To speak of the dream would surely have been seen as treason—it was probably treasonous, on Effie's part, even to have had the dream in the first place. The Trinkets are not a family that can afford to fall in the President's favor, since Mrs. Trinket's father is a Capitol politician whose job depends on being in Snow's good graces.
Six-year-old Effie, of course, does not understand this. Still, she's sufficiently afraid of her mother that the dream is never spoken of again, and the next time she sees Snow, she allows herself to be bounced on the old man's knee just like she knows she's supposed to. Beneath her innocent, happy little-girl smile, though, lies a suppressed shiver when Snow kisses her cheek and her nose catches the reek of blood disguised beneath the mint on his breath.