I asked this on the big thread about the party and frozen summer. A kind poster posted her trip reports from last year.
She said things were quiet until about noonish.
She had gotten to MK at 8am. She was the only person on her bus from her resort and thought it was a fluke. But the park was just not busy. She rode quite a bit of rides that morning. She also didn't stay straight through the whole day, visiting the park 3 or 4 times in the 24 hour period.
HTH!