what I'm doing wrong here?
Almost everything.
$today = date('Y-m-d'); // no need for strtotime
$sth = $db->prepare("SELECT id_email FROM db WHERE hardcopy = '1' AND hardcopy_date <= :today AND hardcopy_sent = '0' ORDER BY id_email ASC");
$sth->bindParam(':today',$today); // no need for PDO::PARAM_STR
$sth->execute(); // no need for if
$this->id_email = $sth->fetchAll(PDO::FETCH_COLUMN); // no need for while
return count($this->id_email); // no need for the everything else
effectively, you always have your fetched data (in this case in $this->id_email
variable) to tell whether your query returned anything or not. Read more in my article on PDO.