class InOrderTreeIterator {
      Stack stack;
      TreeNode cursor;

      InOrderTreeIterator(TreeNode root) {
          cursor = root;
          s = new Stack;
      }

      bool hasNext() {
          return cursor != null || !stack.empty();
      }

      TreeNode next() {
          if (cursor != null) {
              while (cursor.left != null) {
                  stack.push(cursor);
                  cursor = cursor.left;
              }
          } else if (!stack.empty()) {
              cursor = stack.pop();
          } else {
              throw new NoSuchElementException();
          }
          TreeNode ret = cursor;
          cursor = cursor.right
          return ret;
      }
  }

But it's not obvious to me how you'd write a generic iterator that supports something like finding all free variables in an expression tree, or even just express a tree mapping function that constructs a new tree with the same structure (for example, "make all variables in the expression uppercase"). It's been a while since I worked with iterators so correct me if I'm wrong and this is in fact easy with iterators.

With something like Haskell's recursion-schemes library [0] these operations are all just a few lines long, guaranteed to terminate, and don't need to be updated if your data structure changes (for example you add new expression nodes). I'm not aware of any non-functional programming language that can do that. See for example the freeVars function at the bottom of the linked recursion-schemes doc.

[0] https://hackage.haskell.org/package/recursion-schemes-5.2.3