Snippet to disable "Add to Cart" button if all variations for a WooCommerce product are out of stock

variable-product-disable-add-to-cart-button.php

<?php

add_action( 'woocommerce_single_product_summary', 'replace_single_add_to_cart_button', 1 );
function replace_single_add_to_cart_button() {
    global $product;

    if( $product->is_type( 'variable' ) ) {
        $is_soldout = true;

        foreach( $product->get_available_variations() as $variation ){
            if( $variation['is_in_stock'] )
                $is_soldout = false;
        }

        if( $is_soldout ){
            remove_action( 'woocommerce_single_variation', 'woocommerce_single_variation_add_to_cart_button', 20 );
            add_action( 'woocommerce_single_variation', 'sold_out_button', 20 );
        }
    }
}

// THE SOLD OUT BUTTON REPLACEMENT
function sold_out_button() {
    global $product;

    ?>
    <div class="woocommerce-variation-add-to-cart variations_button">
        <?php
            do_action( 'woocommerce_before_add_to_cart_quantity' );

            woocommerce_quantity_input( array(
                'min_value'   => apply_filters( 'woocommerce_quantity_input_min', $product->get_min_purchase_quantity(), $product ),
                'max_value'   => apply_filters( 'woocommerce_quantity_input_max', $product->get_max_purchase_quantity(), $product ),
                'input_value' => isset( $_POST['quantity'] ) ? wc_stock_amount( $_POST['quantity'] ) : $product->get_min_purchase_quantity(),
            ) );

            do_action( 'woocommerce_after_add_to_cart_quantity' );
        ?>
        <a class="single_sold_out_button button alt disabled wc-variation-is-unavailable"><?php _e( "Sold Out", "woocommerce" ); ?></a>
    </div>
    <?php
} 

?>