Code to schedule a cron to run at a certain local time

gistfile1.php

add_action( 'init', function() {
  /* must have this check here, b/c although a new cron event won't be added without it,
   *the wp_schedule_event() function triggers the action to run immediately, even if
   *set for a different time of day. */

  if ( ! wp_next_scheduled( 'social_delete_posts' ) ) {
    $local_time_to_run = '1am';
    $timestamp = strtotime( $local_time_to_run ) + ( get_option( 'gmt_offset' ) * HOUR_IN_SECONDS );
    wp_schedule_event(
      $timestamp,
      'daily',
      'social_delete_posts'
    );
  }
} );