Filter admin columns by custom post field value

Based on @ Andy Macaulay-Brook comment on your question you can try this (it will add a dropdown next to the Filter button on top of the admin listing table):

add_action( 'restrict_manage_posts',  'filter_dogs_by_color' );

// Filter Dogs by Color
function filter_dogs_by_color( $post_type ) {
        if ( 'dog' !== $post_type ) return;    // Replace 'dog' with your post_type

        $taxonomy = 'color'; // Replace 'color' with your taxonomy slug

        $info_taxonomy = get_taxonomy($taxonomy);
        $selected      = isset($_GET[$info_taxonomy->query_var]) ? $_GET[$info_taxonomy->query_var] : '';

        wp_dropdown_categories(array(
             'show_option_all' => __("Show All {$info_taxonomy->label}"),
             'taxonomy'        => $taxonomy,
             'name'            => $info_taxonomy->query_var,
             'orderby'         => 'name',
             'selected'        => $selected,
             'hide_empty'      => true,
              'value_field'   => 'slug'
         )
        );
}