I would argue that the most important symbol in the novel is the tree. Gene is drawn to it when he returns to Devon in the first chapter, and his description reflects on the influence of the tree on his childhood. He describes as though it is a monster that tormented him as a child, but upon returning, he realizes it is nothing of which to be afraid. The tree has Biblical symbolism- Finny's fall represents the loss of innocence among the boys. When Gene pushes Finny, not only does he lose his innocence by committing an act of violence, but he cause Finny to lose his by shattering his ideal world. To a lesser extent, WWII is also a symbol for loss of innocence in the novel. It connects back to the shattering of Finny's world, which connects back to the tree itself.
The weather is also a symbol in the novel. The weather directly reflects Finny's influence on Gene. When Finny and Gene are happy, and Finny is living his ideal existence, it is summertime. The boys have few obligations, the rules of Devon have been relaxed for the summer session, and there's an idyllic atmosphere to the school. Yet when Finny is gone from Devon, and after he dies, it is winter. There is a coldness, the war has come to the school, and Gene no longer has the friendship of Finny to guide him.