<?php

function cstr_add_cart_item_data( $cart_item_data, $product_id ) {
	if ( isset( $_POST ) && ! empty( $product_id ) ) {
		$post_data = $_POST;
	} else {
		return;
	}

	if ( empty( $cart_item_data['my_field'] ) ) {
		$cart_item_data['my_field'] = array();
	}

	// add my data.

	return $cart_item_data;
}

// Add item data to the cart.
add_filter( 'woocommerce_add_cart_item_data', 'cstr_add_cart_item_data', 10, 2 );