You can visit the Burj Khalifa at anytime of the year or day or night.
The best time though to visit the Burj Khalifa is between 4:00 PM to 6:00 PM or more towards sunset for the best views.
Between the times of 4:00 PM and 6:00 PM is prime hours for the Burj Khalifa and it cost more for reservations during those times.
Before 4:00 PM it will cost less to visit Burj Khalifa but the best views from Burj Khalifa are at sunset which is when I would recommend visiting the Burj Khalifa.