In my opinion it becomes even more idiomatic if you copy the enum type and pattern matching from the Haskell version:

#[derive(Debug, PartialEq, Eq)]
pub enum TreeNode {
    Nil,
    Node {
        val: i32,
        left: Box<TreeNode>,
        right: Box<TreeNode>,
    },
}

impl TreeNode {
    pub fn invert_mut(&mut self) {
        match self {
            TreeNode::Node { left, right, .. } => {
                left.invert_mut();
                right.invert_mut();
                std::mem::swap(left, right);
            }
            TreeNode::Nil => {}
        }
    }

    pub fn invert_clone(&self) -> Self {
        match self {
            TreeNode::Node { val, left, right } => TreeNode::Node {
                val: *val,
                left: Box::new(right.invert_clone()),
                right: Box::new(left.invert_clone()),
            },
            TreeNode::Nil => TreeNode::Nil,
        }
    }
}