We were there Jan 5-13, 2006 with DD5 and DS3. We're in Illinois so we wore medium wt winter coats on the plane and ended up wearing them to the parks 2 days. Two of the days the highs were in the 40s. The rest of the time it was in the 60s or 70s during the day. We dressed the kids in layers- Tshirt, zip-up hoodie, long pants most days. I think they wore shorts all day once.
Look at the 10 day forcast on weather.com for your expected daytime highs. The kids actually went swimming two of the days and we saw people swimming in temps in the 50s. Yikes!
We LOVED going that week!!! The crowds were small and it never rained. The cooler temps allowed us to stay in the parks from opening until 4 or 5pm with no "nap break" and the kids easily kept up with that schedule. (We never did fireworks, but the kids were always in bed sleeping at 8pm and ready to go early the next morning.) Have fun!