I've been to WDW 3 times during Christmas. In 95, 98, and 2000. In 1995, they actually held the live parade on the 25th, because we walked right by Regis in the announcing booth. In 98, they did have a parade on Chistmas Day, but it wasn't live. I believe they tape the Christmas parade early in December for television.
Their are way too many people in the MK on Christmas day, it is a zoo. The MK fills up to capacity rather quickly. If you don't like crowds, you won't like Christmas Day in the MK.
This past Christmas, we went to the MK on the 20th, it was great, not crowded at all. Then we went to the MK on the 27th and it was packed. I think around the 22nd, everyone starts arriving, so the parks are packed from the 22nd to the 1st.
I like going to the MK on New Year's Eve much better.