How to hide webform block for users who submitted the form already?
Have a look at the Rules block visibility module. Here is a quote from its project page:


  The Rules block visibility module allows Rules components to be used to control block visibility. This provides Drupal administrators and developers extreme flexibility in controlling when blocks should be displayed on their websites, in addition to the default visibility options provided by Drupal.
  
  The general idea is that if you can do it with Rules, you can use it to control block visibility, so the possibilities are limitless:
  
  
  Need to show a block only for users registered more than a month ago?
  Perhaps you have a block that must be shown only between 8am-5pm on weekdays?
  What about displaying or hiding a block based on current weather conditions?
  
  
  All of this can be done by using Rules block visibility.


With that, and as per the "if you can do it with Rules, you can use it to control block visibility" above, you may have a possible solution for your question, provided you can think of an appropriate rule to be used for it. Using the Webform integration with Rules, you should be able to catch (=Rules Event) the submission of a form by a user. And combine this with some type of Rules Action so that the form is no longer visible to that user.

For an illustration of how to use this module, refer to my answer to "How to stop a Views block from displaying to admins, such as user/1?".