I'm just about to look this up myself. From what I remember as a kid, it was called a salt dough, but I could be wrong.
Salt Dough it is! I don't have a recipe, but I do have an ornament my mom's best friend made for me for my first Christmas, and I just turned 32! 
If they are kept carefully, they will last a long, long, long time.
Have fun!!!
Here is the recipe I use.
You will need:
1 cup Corn Starch
2 cups baking soda
1 1/2 cups water
In a large saucepan mix corn starch and baking soda. Add water and stir until smooth. Cover and cook over medium heat, stirring occasionally, until mixture is the consistency of slightly dry mashed potatoes. Remove from heat and cover with a damp cloth. When cool enough to handle, coat hands and surface lightly with corn starch and knead until dough is smooth and pliable.
Roll out to 1/4 inch thickness and cut with holiday cookie cutters. To dry, place on a baking sheet in a 250 degree oven for 20-30 minutes or until hard. For best results, allow to cool and brush loose powder off ornaments before painting. Makes about 16-20 ornaments.
Good luck!
Ingredients
Playdough is a classic childhood toy everyone can have fun with, and it's so easy to make at home you'll never buy that stinky store variety again.
Basic ingredient ratios:
2 cups flour
2 cups warm water
1 cup salt
2 Tablespoons vegetable oil
1 Tablespoon cream of tartar (optional for improved elasticity)
food coloring (liquid, powder, or unsweetened drink mix)
scented oils
Applesauce Cinnamon Ornament Dough
Equal amounts cinnamon and applesauce.
You can add a little white glue for stretchiness.
Roll the dough out or press with hands until it is approximately 1/4 inch thick. Let dry naturally or dry in dehydrator, I decorate with fabric paint pens.
The scent will last for at least 3 years.
I love the applesauce ornaments. I am going to make new ones with my kids on Monday as they have no school due to hunting day. I have some of these that are about 6 years old that still smell. You can also add glitter to the dough before rolling them out to add some sparkle.
Applesauce Cinnamon Ornament Dough
Equal amounts cinnamon and applesauce.
You can add a little white glue for stretchiness.
Roll the dough out or press with hands until it is approximately 1/4 inch thick. Let dry naturally or dry in dehydrator, I decorate with fabric paint pens.
The scent will last for at least 3 years.
Wow - this just took me back! I'd forgotten that I had made these several years ago. Thanks for the trip down memory lane!! 
Sorry about that, my grandson likes to push the keyboard keys.
Yes, just roll out and cut with cookie cutters.
I like to put ground allspice, nutmeg, and clove in to replace part of the cinnamon just because they smell good (and I don't use as much of the others in daily cooking so it helps them not get stale.) I can get those quart jars for $4 or less.
They look like gingerbread, so we just decorate them like gingerbread cookies.
Try a Google image search for cinnamon ornament, and there are a lot of ideas there.
These look like frosted cookies (scroll down one) - http://www.tasteofhome.com/Cooking-Schools/Holiday-Crafts-from-our-Festive-in-a-Flash-Cooking-School-Shows
Outlined - http://www.myanonymousblog.com/photos/uncategorized/2007/12/10/img_3791_2.jpg
Stained Glass cookies - http://simplyrecipes.com/recipes/stained_glass_cookies/
'Sugared' cookies - http://www.flickr.com/photos/bluejeanprimitives/2127168694/
Here is the recipe I use that includes elmers glue. I found they hold up a little better than ones without.
1 1/2 cups ground cinnamon
1 cup applesauce
1/4 cup white school glue (like Elmer's)
Bowl
Plastic food wrap
Rolling pin
Wax paper
Cookie cutters or a knife
Ribbon or yarn for hanging
Straw
How to make it:Mix cinnamon, applesauce, and glue together in a bowl. The dough should be as thick as cookie dough. Add a bit of water if the dough is too stiff.
Remove from bowl and knead. Put it back in the bowl, cover with plastic wrap, and let sit for at least a half hour.
Remove the dough, knead again to make sure it's smooth. Flatten/roll the dough between waxed paper until it's between 1/4" thick and 1/8" thick.
Cut out desired shapes, use a straw to punch a hole for the ribbon to hang. The circle of dough will pull out with the straw.
Gently place the shapes on a piece of clean wax paper. They will take 3-5 days to dry, and you will need to turn them over a couple of times a day for them to dry evenly and flat.
Don't be surprised to see that the ornaments get smaller during the drying process. Keep this in mind when you pick out the cookie cutters for your designs. You will also notice that if you do not turn the ornaments over often enough while they are drying, the edges of the ornaments will curl.
When dry, thread a piece of ribbon or yarn through the hole to hang.
SHAPE IDEAS: Tree, Apple, House (gingerbread), Bell, Heart, Goose, Gingerbread Man, Star...
Optional Painting ideas - use acrylic paints or fabric paints to paint details, like white 'frosting' on a gingerbread man or gingerbread house, or eyes on a goose.
I've made those cinnamon applesauce ornaments also. They cut out great. They work really well with those plastic cutters with the details imprinted(Hallmark, Tupperware ect)
Your house will smell wonderful making these! We used puffy paints(aka fabric paint) in the squeeze bottles. I think they still make this. It came in lots of colors and dried with nice dimension. They even had mettallics and glitter also.
This makes the cutest gingerbread people. I've had mine for many years. You can give them a light sanding on the back if they have lost their smell if they weren't sealed with anything.
This is the time to purchse the cheapest cinnamon you can find. You don't want to use your Penzey's finest here unless money is no object!
I checked the taste of home page mentioned. That's the look I had in mind, but with the ability to put thinner & smaller details with the paint. I like how the foundation paint looks thick, like icing. That can be achieved with something like puffy paint, correct? I was thinking I could put the same thicker paint in a bag with a tip for the details.
Am I on the right track??
Thanks for all the suggestions!!!!
I made cinnamon ornaments a couple of years for party favors for my children's christmas parties at school.... they were always big hits. I did not do ANY decorating to them though...... I just used a decorative cookie cutter that made impressions on most of them, although we also did some plain stars, and simple shapes. I bought my cinnamon at Sam's in the large containers because I was making several....... We enjoyed them for several years and may still have a few in the Christmas boxes but they no longer smell.
I bet they would be really cute with details painted on. My daughter loves gingerbread men - so they were simple and cute left plain.....
Jaimelt76 your kids actually have the day off to go hunting? My husband will wish that we lived there when our kids were young.
Michigan schools here in the U.P. take off for the first day of hunting season. It has been that way since I was in school. It is crazy the days they get off for.
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