I can't speak to the first half of that week right by New Years, but I've arrived on 1/4 with our first park day being 1/5. At the time I thought crowds were more than I'd expected, though still manageable. However, that was in 2017 and was my first trip since 2009. I went again this year during a less-busy week in early May and realized that the crowd levels in early January weren't bad at all, my expectations were just off because I was basing it on trips from a decade or more ago.
Looking at it now, I'd say those dates were very reasonable crowd-wise if you have your expectations set right. I'd imagine the days closer to New Years would be a bit busier as you wait for the holiday crowds to leave.