Nevermind, figured it!
For anyone else with the same question we needed to use: get_post_type( get_the_ID() ) and set it as a variable.
Eg:
<?php
$post_type = get_post_type( get_the_ID() );
if ( $post_type == 'horses'):?>
<a href="<?php the_permalink(); ?>"><?php the_title(); ?>
<?php else:?>
<?php the_title(); ?>
<?php endif;?>
