Although I've never been to WDW before 1/1, I have checked in on 1/1 (and will again this year) for that very first week in January. Crowds thin out amazingly fast! And this coming year, I think there are many schools which go back 1/3, so I'm counting on it again. The only downside can be the weather-whenever I've gone that first week of January for the last few years, it's been very cold! Bring your hats and gloves-they sold out at the parks very fast and were very expensive. Also, if there are any Christmas decorations you really want to see, get there fast. It's incredible how quickly a huge display can disappear. One year I went to Epcot 1/2 and saw the big Christmas tree between FW and WS along with all its side decorations. Two days later-Poof! It was all gone-I didn't think it was possible to take it all down that fast!