They do have a special Christmas Parade but it only happens at MVMCP. You will need a special ticket to get in. If you are interested in going you should really get you tickets ASAP because the DO sell out. Very much worth every penny!!!!!!!
The MK Christmas Parade is run during MVMCP. Once the Christmas party is over, they run the same parade in the park during the day instead of the Share a Dream Come True parade or other afternoon parade. So about Dec 20, the Party parade becomes the daytime parade through the holiday season.