DCA will close early on those nights. The park is cleared. After the park is readied for the event, ticket holder for Mickey's Halloween Treat are allowed back in. That way special event ticket holders have the park to themselves.
The park will probably close around 5pm. Someone here can verify this for me. I never paid attention to the closing time for this event. I have gone every year they have had this event. If you want to stay in the park for all your nights, then yes you would have to pay for the 5 nights. You will only need one night. The park is open during the day and you should be able to experience most attractions during that time and those days where MHT is not held, the park will stay open regular hours.