Once the Very Merry Christmas Parties are over, they start running the Christmas parade at 3PM in the MK. So, somewhere around Dec 22 or so, they should start having the same parade in the daytime that they had at the party at night. This parade runs until about Dec 31 or Jan 1. Then it goes back to the regular 3PM parade.
If you want a front row spot to watch the afternoon parade, you may need to stake out your spot no later than an hour before, maybe even earlier on Christmas.
Or you can watch the Christmas Day parade from the comfort of your resort room around 10 AM or so. If the local ABC affiliate runs the parade that morning.