Snow foaming, or any other basic cleaning like that, shouldn't remove the wax, just the dirt on top of it!
A high consistency is needed to remove the wax with snow foam, however depending on the product and appliance, it's likely it won't ever remove all the wax, and that's where flaying comes in to remove any excess wax.
Snow foam is used in lower concentrates to remove all the dirt on top of the wax. Done correctly you can essentially clean the car without a mitt and bucket.