When writing a letter to a character, in this case one found in The Hunger Games, one needs to choose a character to which they relate to, sympathize with, or have questions concerning. The following suggestions are provided for you to examine in order to choose and focus your letter to one of the characters.
A letter to Katniss could explain how you feel about the choices she made, the challenges she faced, and how you feel her choices benefited her or failed to benefit her.
A letter to Peeta could explain, again, how you saw his character over the course of the novel. You would be sure to explain how you felt about the choices he made and how you feel about what happened to him in the games.
A letter to Gale could explain how you feel about his behavior and what yo think he should do about his relationship with Katniss. A full explanation of your feelings need to be stated in order to justify your stand.
You should write it to Peeta because he is a really interesting character in the book.