Wordpress - Add custom taxonomy fields when creating a new taxonomy

Solved!

add_action( 'create_category', 'save_extra_taxonomy_fields', 10, 2 );   

Props to the Category Meta plugin. I downloaded various category meta plugins from the WP repo, and this one has the ability to add the meta data on the Add New screen. I dug through the code and found the elusive create_{term} hook.

I think the tutorial you referenced was great and I've based this code off it. It stores the metas for taxonomy menu_category on the add and edit forms for that taxonomy, and displays it in the edit form. The options table entry would be taxomomy_24_metas for the term id 24.

add_action('menu_category_edit_form_fields','menu_category_edit_form_fields');
add_action('menu_category_add_form_fields','menu_category_edit_form_fields');
add_action('edited_menu_category', 'menu_category_save_form_fields', 10, 2);
add_action('created_menu_category', 'menu_category_save_form_fields', 10, 2);

function menu_category_save_form_fields($term_id) {
    $meta_name = 'order';
    if ( isset( $_POST[$meta_name] ) ) {
        $meta_value = $_POST[$meta_name];
        // This is an associative array with keys and values:
        // $term_metas = Array($meta_name => $meta_value, ...)
        $term_metas = get_option("taxonomy_{$term_id}_metas");
        if (!is_array($term_metas)) {
            $term_metas = Array();
        }
        // Save the meta value
        $term_metas[$meta_name] = $meta_value;
        update_option( "taxonomy_{$term_id}_metas", $term_metas );
    }
}

function menu_category_edit_form_fields ($term_obj) {
    // Read in the order from the options db
    $term_id = $term_obj->term_id;
    $term_metas = get_option("taxonomy_{$term_id}_metas");
    if ( isset($term_metas['order']) ) {
        $order = $term_metas['order'];
    } else {
        $order = '0';
    }
?>
    <tr class="form-field">
            <th valign="top" scope="row">
                <label for="order"><?php _e('Category Order', ''); ?></label>
            </th>
            <td>
                <input type="text" id="order" name="order" value="<?php echo $order; ?>"/>
            </td>
        </tr>
<?php 
}

You can add custom field to the add new term page screen through following hooks:

1. {taxonomy_name}_add_form_fields
2. {taxonomy_name}_edit_form_fields
3. edited_{taxonomy_name}
4. create_{taxonomy_name}