Why this code doesn't send an email with drupal_email()?
The answer's in your comments

//Therefore the first argument is  'mailform_form'


But you're using the string mailform as the first argument.

If your module is called mailform_form as your comments suggest, use this code:

drupal_mail('mailform_form','some_mail_key', $valid_email, language_default(), $params, $from, TRUE)


If it's named mailform, use your original call to drupal_mail, but change the name of your hook function to the correct one:

function mailform_mail($key, &amp;$message, $params) {