I'm not sure how many kids actually have their birthdays on Christmas, but I can tell you from experience that having a birthday anywhere within the 2 weeks before and after means that you get ripped off with the whole presents and party deal. I think this means that you have to try extra hard to make the birthday special amidst all of the other excitement going on.
After reading YogaMum's account of making gingerbread houses with her kids, I thought yes, it sounds like a mess, but I often make just as much of a mess by myself... and how much fun did those kids have?? So I think especially around Christmas making gingerbread houses at a birthday party would be awesome. (Probably splitting kids into groups of 3 or 4 and having an adult at each house would help with the damage control and sharing issues. Recruit some friends to drink some nog and eat some candy with you!)
When I was a kid our family had a collection of cast iron molds for cookies and cornbread and a gingerbread house mold like this one. It was pretty great because it had trees and other accessories besides just house walls and roof. From what I hear, you can also buy one-time kits at Trader Joe's and Ikea. Also, if you're super talented, you could just roll out some dough and design your own house from scratch. I'd suggest this if you are an engineer, an artist, an architect, or anything but a perfectionist. :)
Suggested toppings: anything really, but red hots, gumdrops, mini candy canes, peppermints, sprinkles of all colors, etc. are the common adornments. To truly make this party a birthday party and not just a Christmas party, I'd suggest adding some food coloring to the royal icing to make different color options and branching out from the traditional candy to include tootsie rolls, Nerds, that candy that's shaped like fruit—what's that one called??—anything to make it more fun and more just a big candyfest instead of Christmas: