Events are visible (OPEN) once they have an opportunity attached to them.
If you do not want them to appear in the volunteers search results then you can CLOSE the event. This can easily be RE-OPENED at a later date.
How To Close An Event
[ADMIN MENU] Opportunities & Providers > Events
Next to your opportunity press the CLOSE icon. The event will no longer by visible at the top of the volunteers search results.
NOTE: Closing an event does not effect whether the opportunities are visible in the search results. The visibility of EVENTS and OPPORTUNITIES are independent from each other.