The Date the activity happened field appears within a survey by default.
When creating a new survey it is listed on the right in the Your Survey Questions column
If the Date Happened field has been removed from a survey, it will appear on the left in the Public Questions Library when on the Survey Editor page
Click the Add button to add it to the Survey
Once the Date Happened field has been added to the survey, it can be used while creating/editing a story or submitting a survey response: Date Happened: change the date stamp of a story or survey response