O.K. I totally swear this was going to be my first post on this topic and I am not copying the idea from Posie, but I'm afraid her post today came out before mine and she has lovely pictures to go with it, so I will send you over there to see the paper balloons/ light shades. But be sure to come back for the rest here, because my idea is more than just the little waterbombs. (And for lightshades, you can also use paper cranes.)
My first activity suggestion is origami in general. All you need to make it a holiday activity is use paper in Christmas and/or winter colors and/or designs (which includes white for snow, and copier paper or printer paper works wonderfully), and find a good book of directions at your library. There are even directions for several projects to be found on the web. My favorite things to fold are boxes, especially boxes with lids. My best origami book is one I bought on clearance at Border's a few years ago. It is called The Origami Handbook by Rick Beech. Another book that has a few nice origami projects in it is The Complete Book of Papercrafts published by Hermes House. My favorite online resource is Karen Thomas on the Carol Duvall show. And don't forget kirigami! This is like origami, but includes the use of cutting to make the figures and shapes. Often it is just a few little snips that make all the difference, like a tree with a star.
You can do this, I'm sure. As soon as a kid can follow step-by-step pictures (ask any little boy with a new Lego set) that kid can make origami. For mine it was around six years old. It does take some practice to get the folds precise enough for a polished outcome. Try a paper cup for starters, and then be daring! You just need to find a book with good, basic instructions and diagrams. And a popsicle stick works well as a bone folder tool.
We have dozens of completed projects around the house. I will take photos if anyone wants to see some of them.