Conditional statement for if archive page has posts which contain certain taxonomies/categories/tags, show those terms

I am using Isotope to filter posts on the fly from my archive pages.

I have a Custom Post Type called “art”. On the sidebar, I’ve created links to yearly archives on my sidebar, i.e. 2014, 2013, 2012… etc.

When I am on a yearly archive page, i.e. /art/2012, I want only the terms which exist for this custom-post-type on this year’s archive page to appear.

For example, if I am on the date archive of 2009, I only have drawings, not paintings, so I only want the category “Drawings” to show, as clicking “Paintings” will yield zero results (hence the redundancy).

The code I have currently on my sidebar.php (outside the loop) is a modified version that I found here which simply makes wordpress regurgitate all categories across all post types, which is not what I want:

<ul id="filters" class="menu filter">
    <li><a href="#" data-filter="*">All</a></li>

    <?php // Verify if tag/cat is used in archive: https://wordpress.stackexchange.com/a/31981/32287
    $categorys = get_categories(
                    array(
                    'type' => 'art',
                    'exclude' => '1,5',
                    'hide_empty' => false
                    ) 
    );
    if ($categorys) {
        foreach ($categorys as $category) {
            echo '<li>';
            if($category->count > 0){ // check cat count
                    echo '<a href="#" data-filter=".category-' . $category->slug . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name . '</a></li>';
            } else { // if no posts
            }
        } // end foreach
    } // end if
    ?>
</ul>

Can anyone help me write a function which will output the terms that only exist for the yearly date archive page of custom post type “Art”? Been googling for days without avail. 🙁