You can almost complete Chapter 3 on the first day. If you're quick about it, you can finish the first six required missions of the chapter (Jealous Johnny, Bait, Wrong Part of Town, Tagging, Lola's Race, and The Tenements) all on Christmas Eve. However you will not be able to attempt The Rumble on Christmas Eve (even if you have finished The Tenements early enough in the day).
I don't know, for some reason I thought that maybe you could skip Christmas is Here the same way you can skip The Big Prank. But no, Christmas is Here is indeed a required mission and must be completed before The Rumble becomes available. So there is no way to avoid the mother's ugly-ass sweater.
