Great question! Yes, in addition to being able to view the parade on tv, Disney World and Disneyland are open. Here's a listing of the parks' hours.
Magic Kingdom - 8:00 a.m. to 1 a.m.
Animal Kingdom -8:00 a.m. to 9 p.m.
Epcot - 10:00 a.m. to 9:30 p.m.
Hollywood Studios - 8:00 a.m. to 10:00 p.m.
Blizzard Beach - 10:00 a.m. to 5:00 p.m.
Typhoon Lagoon - Closed until January 5th, 2013
Downtown Disney - 8:00 a.m. to 2:00 a.m.
Disneyland Park - 8:00 a.m. to 12:00 a.m.
Disney California Adventure Park - 8:00 a.m. to 11:00 p.m.
Be warned though that the parks have sometimes reached visitor capacity on Christmas Day around 11a.m., unable to let additional guests in. Magic Kingdom usually gets the most crowded on Christmas!