The feature of creating custom fields for products is baked right into WooCommerce, whether to implement it directly in functions.php or do the same via a plugin is left to one's sole discretion.
Remi Corson has written an excellent article detailing the same.
Here's the gist :
1.Create the fields using the woocommerce_product_options_general_product_data hook
add_action( 'woocommerce_product_options_general_product_data', 'woo_add_custom_general_fields' );
function woo_add_custom_general_fields() {
// Define your fields here.
// You can create text, textarea, select, checkbox and custom fields
}
2.When product is saved save the value entered in your custom field using woocommerce_process_product_meta hook
add_action( 'woocommerce_process_product_meta', 'woo_add_custom_general_fields_save' );
function woo_add_custom_general_fields_save( $_post_id ) {
//save field values
}