Green represents envy. Perhaps the speaker feels jealousy toward the one Forrest is with.
This line is meant to represent the growth, increasing intimacy, etc. in the relationship between Frank and Forrest. It can been seen as the “good times” in their relationship. The next line, however, contradicts this line by referencing the bad times in the relationship.
And uh, you know, a forest of trees is also literally green.
To help improve the meaning of these lyrics, visit "Forrest Gump" by Frank Ocean Lyrics and leave a comment on the lyrics box