We went last year from the 2nd to the 12th, and it was still extremely crowded the first few days of our trip. After about the 4th the crowds thinned out considerably, and by the end of the trip, they were practically non-existent. It may have been a result of the way the holidays fell last year however. I think New Year's Day fell on a Saturday, so the crowds didn't leave as early as they normally do.
Based on last year though, we decided to plan our upcoming trip for the second week in January this time around. Even if the parks are still crowded, I'm sure you'll have a great time. Just don't go that week expecting the holiday crowds to have disappeared and you won't be disappointed. Have fun!
