This code adds hidden fields to the Ultimate Member registration form.

add_a_hidden_field_to_register.php

<?php

// Add hidden fields you need to this array.
$GLOBALS['um_registration_extra_data'] = array(
	'field_key_1' => 'abc',
	'field_key_2' => 'xyz',
);

// This code adds hidden fields to the form.
add_action( 'um_after_register_fields', 'add_a_hidden_field_to_register', 10, 1 );
function add_a_hidden_field_to_register( $args ) {
	foreach ( $GLOBALS['um_registration_extra_data'] as $key => $val ) {
		echo '<input type="hidden" name="' . esc_attr( $key ) . '" value="' . esc_attr( $val ) . '" />';
	}
}

// This code saves hidden field values on the form submit.
add_action( 'um_registration_set_extra_data', 'save_hidden_field_on_redistration', 10, 3 );
function save_hidden_field_on_redistration( $user_id, $args, $form_data ) {
	foreach ( $GLOBALS['um_registration_extra_data'] as $key => $val ) {
		if ( isset( $args[ $key ] ) ) {
			update_user_meta( $user_id, $key, sanitize_meta( $key, $args[ $key ], 'user' ) );
		}
	}
}

This gist is a part of the article Add a hidden field to your register form.

You can add this code to the functions.php file in the active theme directory. Skip the opening <?php tag.