Wordpress - Remove the category/taxonomy description field?

When no hook is available, you can always count on the old jQuery trickery...

add_action( 'admin_footer-edit-tags.php', 'wpse_56569_remove_cat_tag_description' );

function wpse_56569_remove_cat_tag_description(){
    global $current_screen;
    switch ( $current_screen->id ) 
    {
        case 'edit-category':
            // WE ARE AT /wp-admin/edit-tags.php?taxonomy=category
            // OR AT /wp-admin/edit-tags.php?action=edit&taxonomy=category&tag_ID=1&post_type=post
            break;
        case 'edit-post_tag':
            // WE ARE AT /wp-admin/edit-tags.php?taxonomy=post_tag
            // OR AT /wp-admin/edit-tags.php?action=edit&taxonomy=post_tag&tag_ID=3&post_type=post
            break;
    }
    ?>
    <script type="text/javascript">
    jQuery(document).ready( function($) {
        $('#tag-description').parent().remove();
    });
    </script>
    <?php
}

Use CSS, I was implementing the JS solution and I didn't like the delay, then I've remembered about this.

body.taxonomy-name .term-description-wrap {
  display:none;
}

AFAIK, you can add new fields but you cannot remove the old ones! They are directly printed, and not stored in a variable to which a filter can be applied. Ref: wp-admin/edit-tags.php, line no. 380.