You need to alter the submit callback using the "hook_form_alter" hook to define your own callback :
function mymodule_form_alter(&$form, &$form_state, $form_id) {
if($form_id == 'poll_view_voting') {
$form['vote']['#submit'] = array('_my_poll_submit');
}
}
then you copy paste the code from the "poll_vote" function (in the "poll.module" file) in your callback function and you change the message as needed:
function _my_poll_submit(&$form, &$form_state) {
$node = $form['#node'];
//etc ...
//and at the end:
drupal_set_message(t('My text for your vote was recorded.'));
}