I know this is a super old thread, but I'v been learning how to alter form elements and add classes. I got around to making a custom module:

function yourtheme_custom_form_alter(&$form, &$form_state, $form_id) {
 case'webform_number_whatever':
   _yourtheme_form_add_wrapper($form['submitted']['yourfieldhere'], array('form-field-some-style', 'not-label', 'whatever-other-styles-you-want'));
 break;
}

function _yourtheme_form_add_wrapper(&$element, $classes = array(), $type = array('form-item', 'form-type-textfield'), $removeTitle = FALSE){
  $element['#prefix'] = '<div class="' . implode(" ", $classes) . '"><div class="' . implode(" ", $type) . '">';
  $element['#suffix'] = '</div></div>';
}

To Change the "wrapper" you need to override form_element. Basically all form elements get rendered with the form_element theme theme_form_element($element,$value); (form.inc file)

So to change how this renders your form elements you simply copy that function to your template.php folder and rename it to: phptemplate_form_element($element,$value)

now you can make any changes and they will be used instead of the original function

1. Copy theme_form_element($element,$value); from form.inc
2. Paste it into (your theme) template.php
3. rename it to: phptemplate_form_element($element,$value)
4. clear all theme cache
5. make whatever changes you want and they will be used.

Importantly, theme_form_element will only modify the direct parent wrapper div and this may not be the intended target for CSS effects.

[Although not programmatic, if one simply wants to apply a class to a node field's top-wrapper (it's wrapper's, wrapper's, wrapper) one can I suppose use "Field group" module by selecting "Manage Fields" for a particular content type and select "Add new group" as a simple DIV. Then the label can be removed and desired classes assigned to the additional wrapper (but now we have even more wrappers) - with unlimited nesting]

You could use

'#prefix' => '<div class="new_class">', '#suffix' => '</div>'

and this will wrap it around

Make wrapper attributes configurable!

Create your own form-element theme function in your theme... sites/all/themes/MY_THEME/theme/form-element.theme.inc

function my_theme_form_element($variables) {
  $element = &$variables['element'];

  $attributes = isset($element['#my_theme_wrapper_attributes']) ?
    $element['#my_theme_wrapper_attributes'] : array();

  ...

  $output = '<div' . drupal_attributes($attributes) . '>' . "\n";

  ...
}

Then you can do stuff like this...

function my_module_form_alter(&$form, &$form_state, $form_id) {
  $form['account']['mail']['#my_theme_wrapper_attributes']['class'][] = 'form-field--inline';
}

There are come cases in which neither #prefix/#suffix nor #attributes => array('class') give the desired results. My particular case is adding a class to the ajax-wrapper div around a managed_file element. #prefix/#suffix creates a new container and #attributes/'class'modifies the class of an inner element, not the outermost.

The normal outermost div is just

<div id="edit-doc1--XX-ajax-wrapper">

which is difficult to target in CSS. I can target [id^="edit-doc"] or [id$="-ajax-wrapper"] but both of these target more than just the elements I wanted.

The solution I came up with is to add a #process element to the form and manually manipulate the element's code. Here's the #process attribute added to the form item's declaration:

$form['doc1'] = array(
  '#type' => 'managed_file',
  '#process' => array('mymodule_managed_file_process'),
);

And here's the mymodule_managed_file_process() function:

function mymodule_managed_file_process($element, &$form_state, $form) {

  // Call the original function to perform its processing.
  $element = file_managed_file_process($element, $form_state, $form);

  // Add our own class for theming.
  $element['#prefix'] = str_replace(
    'id=',
    'class="managed-file-wrapper" id=',
    $element['#prefix']
  );

  return $element;
}

Relying on string substitution isn't very portable, so use str_replace at your own risk. This code, however, does indeed alter the outermost DIV to add the necessary class:

<div class="managed-file-wrapper" id="edit-doc1--XX-ajax-wrapper">