Show site content based on user role

You have errors in the code

First, you are using current_user_can() function the wrong way. It has two parameters — $capability and $object_id. You don’t need the latter one, so, in your case:

current_user_can('subscriber')

In my opinion, it’s better to use capability instead of user role in this function. For example, subscribers can’t edit posts, unlike other user roles, so I’d change 'subscriber' to 'edit_posts':

Second, the if condition. Your code says that user must be logged in OR his role must not be a subscriber. It should sound like the user must be logged in AND must be not a subscriber.

add_filter( 'wpmenucart_menu_item_wrapper', 'wpmenucart_hide_for_visitors', 10, 1 );

function wpmenucart_hide_for_visitors( $menu_item_li )
{
    // user is logged in AND his role is higher than a subscriber
    if ( is_user_logged_in() && current_user_can('edit_posts') ) {
        return $menu_item_li;
    } else {
        return;
    }
}

See current_user_can in the Codex.