To change views exposed date filter to month only.

/**
 * Impliments hook_form_views_exposed_form_alter
 *
 */
function exposed_date_filter_form_views_exposed_form_alter(&$form, $form_state) {
   $view = $form_state['view']->name;
   $view_array = array('story', 'news');
   if(in_array($view, $view_array)) {
    // Switch date formatter to month only
     if($form['field_date_value_1']['value']['#type'] == 'date_select') {
          $form['field_date_value_1']['value']['#date_format'] = 'm';
         // Add extra validator to handle filter submit
         $form['#validate'][] = 'exposed_date_filter_views_exposed_form_validate';
      }

      if($form['field_date_3_value_1']['value']['#type'] == 'date_select') {
         $form['field_date_3_value_1']['value']['#date_format'] = 'm';
         // Add extra validator to handle filter submit
         $form['#validate'][] = 'exposed_date_filter_views_exposed_form_validate';
      }

      if($form['field_date_2_value_1']['value']['#type'] == 'date_select') {
         $form['field_date_2_value_1']['value']['#date_format'] = 'm';
         // Add extra validator to handle filter submit
         $form['#validate'][] = 'exposed_date_filter_views_exposed_form_validate';
      }
  }
}

/**
 * Custom validator for exposed date filter
 */
function exposed_date_filter_views_exposed_form_validate(&$form, &$form_state) {
$handlers = &$form_state['view']->filter;
  foreach ($handlers as $key => $handler) {
    if (!empty($handler->options['exposed'])
     && isset($form[$key]['value']['#type'])
     && $form[$key]['value']['#type'] == 'date_select'
     && $form[$key]['value']['#date_format'] == 'm'){
      $handler->options['granularity'] = 'month';
      $handler->format = 'm';
    }
  }
}