Query a custom taxonomy for certain posts

You are setting your taxonomy arguments incorrectly in WP_Query. You need to set up a tax_query, which takes an array of arrays. See the codex.

$args = array(
    'post_type' => 'post',
        'orderby' => 'rand',
    'tax_query' => array(
        array(
            'taxonomy' => 'newsdates',
            'field' => 'id',
            'terms' => $field
        )
    )
);