I visited the south rim for Christmas 2015. It was great, I was able to get a campsite inside the park without a reservation (they had plenty of sites open).
I'll note, these were full hookup sites, but the water and sewer were locked out due to the temperature... so just electric and cable tv worked.
Everything was busy, but not super crowded.
As I was leaving, the hordes were arriving. The week between xmas and new years is prime time for families I imagine, the traffic was backed up for miles and miles waiting to get into the park.
2013 KZ Sportsmen Classic 200, 20 ft TT
2020 RAM 1500, 5.7 4x4, 8 speed