Finally did it. With the update of WooCommerce, which I assumed, the syntax of the set price did change. Function now looks like this:
add_action( 'woocommerce_before_calculate_totals', 'calc_ferienspiele_discount' );
function calc_ferienspiele_discount( $cart_object ) {
global $woocommerce;
$items = $woocommerce->cart->get_cart();
$x=0;
$custom_price = 140; // This will be your custome price
foreach ( $cart_object->cart_contents as $key => $value ) {
$target_product_id=$value['data']->get_sku();
for ($_i = 1; $_i <= $value['quantity']; $_i++) {
$x++;
if ( $target_product_id=='01010101' ) {
if ($x>1) {
$value['data']->set_price($custom_price);
echo 'This works and get displayed';
}
}
}
}
}