What if I need to show a field in node/add but unset or hide it in node/edit?

Could I create a little module with something like...this?

<?php
/**
* Implementation of hook_form_alter().
*/
function MY_MODULE_form_alter(&$form, $form_state, $form_id) {
  if ((arg(0) == 'node') && (arg(2) == 'edit')){
  $node = node_load(array('nid' => arg(1)));
  //want to unset a specific field at the node/edit form (and NOT at node/add)
  unset($form['field_FIELD_NAME']);
  //want to unset the button "delete"
  unset($form['buttons']['edit-delete']);
  }
}
?>

Sorry for the typo...

Yes, I think that the possibility to manage forms using template.tpl shouldn´t be eliminated. This module provides a tpl form... maybe adapting it according to it´s name?

Thanks!!
Rosamunda

Maybe something can be done aading some Rules (with Rules module...)?

I´ve tried with rules, and it successfully managed it.
But the problem remains unsolved because sometimes people could need for this module to take care of the node/add form but not the node/edit form.

Let me explain:
I´ve created a special tpl to edit the form of a specific nodetype.

in template...
....
'page_node_form' => array(
'template' => 'edit-page',
'arguments' => array('form' => NULL),
    ),
....
.....
......
function clearblue_preprocess_page_node_form(&$variables) {
  $variables['intro_text'] = t('');
  $variables['rendered'] = drupal_render($variables['form']);
} 

And I´ve created the file according to what I specify in template.tpl.
In that file, I want the form to appear normally inside node/add, but to hide all values in node/edit unless you´re the admin.
That works OK, but in node/add the settings inside /admin/content/node-type/page/form dissapear, I mean, the form is shown in the ugly normal default way.

<?php 
// Use the normal form in node/add
if ((arg(0) == 'node') && (arg(1) == 'add')){
$node = node_load(array('nid' => arg(1)));
return $messages;
return $rendered;
}

global $user;
// The node/edit form will appear only to admins
if (is_array($user->roles) && in_array('admin', $user->roles)) {
// This code will control only node/n/edit and NOT node/add
if ((arg(0) == 'node') && (arg(2) == 'edit')){
  $node = node_load(array('nid' => arg(1)));
return $messages;
return $rendered;
}
} 
else {
// but if you´re not an admin...
print '<h3>Oops! You cannot edit this content.</h3>';
}
?>

Yes, I know that the edit perm is available bu default, but if you enable organic groups and want the groups to be private (so you need to OG perm to take control), the group manager will be able to edit all content inside a group, no matter what you do to prevent it. OG perms override normal default perms.

What Can I do? Any suggestions?

THANKS!!!

Rosamunda