Hiding taxonomies with no children WP_Query & tax_query

I have this code which has taken over 7 hours to put together through research but the last hours or so I have hit a brick wall!

I require the taxonomy title to be hidden if there are no posts associated with it.

Here is the page: http://cb.dannycheeseman.me/wine-menu/usa/california/

Here is my code:

/**********************************************/
//  CUSTOM WINE MENU SHORTCODE
/**********************************************/


add_shortcode( 'wine_list_per_cat', 'wine_list_per_cat' );

function wine_list_per_cat($atts){

    global $woocommerce_loop;

    extract(shortcode_atts(array(
        'cat' = '',    // list of categories in the format 0,1,2,3,4
        'tax' = 'product_cat', // taxonomy use
        'per_cat' = '3',   // max featured items to display per category
        'columns' = '3',   // columns size
    ), $atts));
?

ul id="wine-menu"

    ?php  

        $wine_type_terms = get_terms( 'wine-type' );

        foreach ( $wine_type_terms as $wine_type_term ) {

            $args = array(
                'post_type' = 'product',
                'showposts' = -1,
                'tax_query' = array(
                    'relation' = 'IN',
                    array(
                        'taxonomy' = 'wine-type',
                            'field' = 'slug',
                            'terms' = array( $wine_type_term-slug ),
                        ),
                        array(
                            'taxonomy' = 'product_cat',
                            'field' = 'slug',
                            'terms' = $cat
                        )
                    ));

            $wine_type_query = new WP_Query($args);?
            li
            h2?php echo $wine_type_term-name; ?/h2
            ul
                ?php  while ( $wine_type_query-have_posts() ) : $wine_type_query-the_post();global $product ?
                    li class="wine-item" 
                        h3?php the_title(); ?/h3
                        span class="wine-bottle-size"Size: ?php echo get_post_meta( get_the_ID(),'wine_bottle_size', true );?/spanbr/
                        span class="wine-percentage"Percentage: ?php echo get_post_meta( get_the_ID(), 'wine_percentage', true );?/spanbr/
                        span class="wine-year"Year: ?php echo get_post_meta( get_the_ID(), 'wine_year', true );?/spanbr/
                        span class="wine-price"Price: ?php echo $product-get_price_html(); ?/spanbr/
                        div class="wine-content"?php echo get_post_meta( get_the_ID(), 'wine_menu_content', true );?/div
                        ?php woocommerce_template_loop_add_to_cart( $wine_type_query-post, $product ); ?
                    /li


                ?php endwhile;?
                ?php wp_reset_postdata(); ?
            /ul


         /li               
        ?php } ?

        ?php wp_reset_query(); ?

/ul!--/.products--
?php } 

UPDATE! OK!!! Woooohooo! Found out what it was.. I should have been calling if have posts before the call for $tax->name; Here is my final, and working code! :)

/**********************************************/
//  CUSTOM WINE MENU SHORTCODE
/**********************************************/


add_shortcode( 'wine_list_per_cat', 'wine_list_per_cat' );

function wine_list_per_cat($atts){

    global $woocommerce_loop;

    extract(shortcode_atts(array(
        'cat' = '',    // list of categories in the format 0,1,2,3,4
        'tax' = 'product_cat', // taxonomy use
        'per_cat' = '3',   // max featured items to display per category
        'columns' = '3',   // columns size
    ), $atts));
?

ul id="wine-menu"

    ?php  

        $taxonomy = get_terms( 'wine-type', array('hide_empty' = true, 'pad_counts' = true));

        foreach ( $taxonomy as $tax ) {

            $args = array(
                'post_type' = 'product',
                'orderby' = 'title',
                'showposts' = -1,
                'tax_query' = array(
                    'relation' = 'AND',
                    array(
                        'taxonomy' = 'product_cat',
                        'field' = 'slug',
                        'terms' = $cat,
                        'operator' = 'IN'
                    ),
                    array(
                        'taxonomy' = 'wine-type',
                        'field' = 'slug',
                        'terms' = array( $tax-slug ),
                        'operator' = 'IN'
                    ),

                ));

            $wine_type_query = null;

            $wine_type_query = new WP_Query($args);

            if( $wine_type_query-have_posts() ) : ?

                li id="wine-type"
                    h2?php echo $tax-name; ?/h2

                    ul
                        ?php while ( $wine_type_query-have_posts() ) : $wine_type_query-the_post();global $product ?
                        li class="wine-item" 
                            h3?php the_title(); ?/h3
                            span class="wine-bottle-size"Size: ?php echo get_post_meta( get_the_ID(),'wine_bottle_size', true );?/spanbr/
                            span class="wine-percentage"Percentage: ?php echo get_post_meta( get_the_ID(), 'wine_percentage', true );?/spanbr/
                            span class="wine-year"Year: ?php echo get_post_meta( get_the_ID(), 'wine_year', true );?/spanbr/
                            span class="wine-price"Price: ?php echo $product-get_price_html(); ?/spanbr/
                            div class="wine-content"?php echo get_post_meta( get_the_ID(), 'wine_menu_content', true );?/div
                            ?php woocommerce_template_loop_add_to_cart( $wine_type_query-post, $product ); ?
                        /li
                        ?php endwhile;?

                    /ul

                /li 
            ?php endif; wp_reset_query(); ?

    ?php } ?

/ul!--/.products--
?php }