How to schedule the execution of a Rules Action based on a webform submission date field?
I'm not really familiar with Rules but this might be a step in the right direction.

If node:created worked you could give http://drupal.org/project/webform_tokens a try, it should define tokens for your form components, however I'm not sure if the date will be in the correct format.

If it's not in the correct format you could alter it for the compontent in a presave hook.

function hook_webform_submission_presave($node, $submission) {
  // Use dpm() to find out how the date is formatted, and make it into a timestamp.
  $date = strtotime($submission-&gt;data['COMPONENT_ID']['value'][0]);
  $submision-&gt;data['COMPONENT_ID']['value'][0] = $date;
}


Now you have altered the data for the submisison, converting a date into a timestamp which should then be used through webform_tokens just like node:created.