Add Country Field to Woo Registration Form

Hi,

i use this Code to hook additional Fields:

/**
 * Hook additional Registration Fields
 */

function wooc_extra_register_fields() {?>
       <p class="form-row form-row-first">
       <label for="reg_billing_first_name"><?php _e( 'First name', 'woocommerce' ); ?><span class="required">*</span></label>
       <input type="text" class="input-text" name="billing_first_name" id="reg_billing_first_name" value="<?php if ( ! empty( $_POST['billing_first_name'] ) ) esc_attr_e( $_POST['billing_first_name'] ); ?>" />
       </p>
       <p class="form-row form-row-last">
       <label for="reg_billing_last_name"><?php _e( 'Last name', 'woocommerce' ); ?><span class="required">*</span></label>
       <input type="text" class="input-text" name="billing_last_name" id="reg_billing_last_name" value="<?php if ( ! empty( $_POST['billing_last_name'] ) ) esc_attr_e( $_POST['billing_last_name'] ); ?>" />
       </p>
	   <p class="form-row form-row-wide">
       <label for="reg_billing_country"><?php _e( 'Land', 'woocommerce' ); ?><span class="required">*</span></label>
       <input type="text" class="input-text" name="billing_country" id="reg_billing_country" value="<?php if ( ! empty( $_POST['billing_country'] ) ) esc_attr_e( $_POST['billing_country'] ); ?>" />
       </p>
       <div class="clear"></div>
       <?php
 }
 add_action( 'woocommerce_register_form_start', 'wooc_extra_register_fields' );

/**
 * register fields Validating.
 */

function wooc_validate_extra_register_fields( $username, $email, $validation_errors ) {

      if ( isset( $_POST['billing_first_name'] ) && empty( $_POST['billing_first_name'] ) ) {

             $validation_errors->add( 'billing_first_name_error', __( 'Vorname ist erforderlich!', 'woocommerce' ) );

      }

      if ( isset( $_POST['billing_last_name'] ) && empty( $_POST['billing_last_name'] ) ) {

             $validation_errors->add( 'billing_last_name_error', __( 'Nachname ist erforderlich!.', 'woocommerce' ) );

      }
      if ( isset( $_POST['billing_country'] ) && empty( $_POST['billing_country'] ) ) {

             $validation_errors->add( 'billing_country_error', __( 'Feld Land ist erforderlich!.', 'woocommerce' ) );

      }
         return $validation_errors;
}

add_action( 'woocommerce_register_post', 'wooc_validate_extra_register_fields', 10, 3 );

/**
* Save addiotional Field in Database
*/

function wooc_save_extra_register_fields( $customer_id ) {
      if ( isset( $_POST['billing_first_name'] ) ) {
             //First name field which is by default
             update_user_meta( $customer_id, 'first_name', sanitize_text_field( $_POST['billing_first_name'] ) );
             // First name field which is used in WooCommerce
             update_user_meta( $customer_id, 'billing_first_name', sanitize_text_field( $_POST['billing_first_name'] ) );
      }
      if ( isset( $_POST['billing_last_name'] ) ) {
             // Last name field which is by default
             update_user_meta( $customer_id, 'last_name', sanitize_text_field( $_POST['billing_last_name'] ) );
             // Last name field which is used in WooCommerce
             update_user_meta( $customer_id, 'billing_last_name', sanitize_text_field( $_POST['billing_last_name'] ) );
      }
    if ( isset( $_POST['billing_country'] ) ) {
                 // Country input filed which is used in WooCommerce
                 update_user_meta( $customer_id, 'billing_country', sanitize_text_field( $_POST['billing_country'] ) );
          }

}
add_action( 'woocommerce_created_customer', 'wooc_save_extra_register_fields' );

Last Name and First Name is working fine. After the registration, i get the value in my Database. But for country it doesn’t work. What is the reason for this?