First, let's consider what a climax is. In literature, this is the highest point of conflict, after which it is clear how the conflict will be resolved.

The highest point of conflict comes just after Ethan's clash with Zeena when he learns that she has arranged for Mattie to be sent away at once. The next day, Ethan insists on taking Mattie to the train station, and the two confess their feelings of love to each other. They arrive at the sledding hill and share a moment of tenderness and then generate a new idea—to commit suicide together by sledding into the big elm tree.

This is the climax. The two are desperate to be together and don't see a way to financially make that possible. The only way to be together forever is to die together.

Even as they reach this decision, the reader feels great tension about how this will play out. After all, sledding into a tree certainly isn't a guaranteed death, and Ethan's vision of Zeena during that ride down the hill seems an eerie moment of foreshadowing that Zeena isn't out of Ethan's life yet. They successfully crash into the tree but fail in their efforts to die together—and that sets up the resolution.