How to hide a field from anonymous users?
Use the Field Permissions module.


  The Field Permissions module allows site administrators to set field-level permissions to edit, view and create fields on any entity.
  
  Features
  
  
  Enable field permissions on any entity, not just nodes.
  Role-based field permissions allowing different viewing patterned based on what access the user has.
  Author-level permissions allow viewing and editing of fields based on who the entity owner is.
  Permissions for each field are not enabled by default. Instead, administrators can enable these permissions explicitly for the fields where this feature is needed.