Lots of cookies besides cutout/sugar cookies!
Merengues -- put a thumb hole in each one before baking. When cool, fill with melted chocolate.
Super easy -- make marshmallow rice krispy treats, using cornflakes instead. Color w green food coloring and shape into wreaths. Make holly berries w either cinnamon candies or dots of red frosting.
If you really want cutout cookies, I'd make very modern, simple "christmas trees" by cutting long, skinny triangles and decorating them very simply. (I'd probably just make 2 or 3 shades of green and do them in solid colors). I like the Martha Stewart sugar cookie recipe.
But there are lots of christmas cookies that don't need to be cutouts. The chocolate snowflake cookies are yummy and simple, there are fruitcake cookies (check foodtv - the Barefoot Contessa just made them), molasass cookies, mexican wedding cakes... you can put a red or green bow on just about any bag of cookies to make it christmasy.
With your favorite sugar cookie recipe, roll out the dough. Use a glass, cut out big circles. Use a smaller glass, cut out a smaller circle in that. Fill w/ hard candy. Bake.
Or make chocolate snowflake cookies. Very pretty, easy and delicious.
You can also decorate cookies by putting frosting in ziplock bags, snip the corners and decorate.
You can use all kinds of things with sharp-ish edges to use as cookie cutters. A rinsed empty can cuts a clean circle, then you can use it to cut crescents. A bottle cap in the center of the circle - there, you have a nice little wreath. Colored sugar, maybe some frosting and you've got pretty , festive cookies.
Take one small glass to cut a circle. Cut out center hole with plastic soda bottle cap. Cover with green icing and decorate little red holly berries with leaves ... maybe a bow or two.
Use three different size round glasses or caps. Attach circles. Ice in white, put some buttons, eyes, mouth and an orange nose. A bright little scarf around the neck is nice too.
If you have an rectagular food storage container, stamp out dough, cut in half into two triangles... Christmas tree. Or you could just cut a long strip and then cut triangles from thatl Cut a long thin strip and cut off little pieces for the trunk. Decorate in green frosting (chocolate for the 'trunk'). Put a yellow dot on the top for the star, ad dots of various colors or those little round sprinkles for the top of cupcakes as ornaments.
Scroll down this blog to the photos of the Christmast tree. There are little presents under the cookie tree. That is more work than I'd ever do, however, you could cut squares and decorate with bows to make boxed presents.
Just use a round glass and decorate prettily.
Cut out a round face using a glass. cut out a small triangle for a hat and attach. use red frostning for the cap with white trim. Put eyes, nose and white whiskers in icing for a face ... maybe some nice pink cheeks too.
If you don't have a pastry bag, you can buy one of those cans of frosting that have the different pastry tips.
I have a slew of cookie cutters because there was a time I was really into making Christmas cookies.
However, I ain't any type of cook. So the Pillsbury tubes in the fridge section of the supermarket worked just fine. I also used canned vanilla frosting which I used food color to dye for various decorations. The big thing is to be creative. Buy colored sugars and anything else that looks festive for decorating.
Here's some inspiration design-wise
Here's a cool blog (with recipe) for twisting two colors of dough together to make candy canes
Snowman (I suppose you could add a little square piece for a hat
Take a look at this gingerbread man that I'll bet could be done pressing together circles.
Santa ... I don't like the colors but you get the idea
If you scroll to the bottom of this page, you could just skip the face and make santa hats of out triangles
Ornaments (I'd go a little fancier ... sparlkly colored sugar would be good but you get the idea
You could make a snowflake design on a round cookie
Am trying to think what household/kitchen items have a "festive shape" that you could use to cut out cookies other than the obvious circle. But in the meantime, here is how I improvised last year... I couldn't find my cookie press and so made traditional spritz cookies, but just in a ball, flattened with a fork criss-cross like you do with peanut butter cookies. I decorated them with festive colors: maraschino cherry, green & red sugar sprinkles and green & red M&Ms. I thought they looked pretty good for winging it! If I think of something more interesting in the shape department, I'll post again.