How to display an Event's custom field on its registration form
I guess the custom fields for Event are not available in smarty on Event registration form but are available on Event information page. But you can retrieve the custom fields for an Event using api. You can use below snippet in tpl file to get custom field data

{crmAPI var='result' entity='Event' action='getsingle' return="custom_81,custom_82" id=$event.id}


The return value specifies list of custom fields that i would like to retrieve. You can remove return option if you would like to get all the Event data including custom fields. 


  To print you can use {$result} variable eg. in above case i would use
  {$result.custom_81} and {$result.custom_8}


HTH

Pradeep