Liz, I've made both of mrslarkins chewy sugar cookie recipes and they are both wonderful.

I used to bake cookies with the kids at our church every Christmas.. kind of Christmas "kick-off" party. Lots of fun.

One of the things they enjoyed the most, which was also pretty simple: Egg yolk paint. Combine one egg yolk with one teaspoon of water and a little gel food coloring for each color. Let them roll out and cut their own shapes, transfer the shapes to parchment-lined baking sheets (you'll definitely want the parchment; the paint sticks otherwise), give them paint brushes, and tell them to go nuts with it. The color stay true, and they bake up nice and glossy and are completely dry when they come out of the oven.

Will they be eating the cookies on the spot? You can use any sugar cookie recipe and add a half-cup extra flour in order to bypass the chilling step, and you can use any frosting and candy for decorating.

If the kids will be taking the cookies home or if the cookies will be used as ornaments, you'll want a sturdier cookie--use a recipe for graham crackers (or purchase a box!) or gingerbread cookies and omit the spices. Roll out the dough no thinner than 1/4".

It might be easier to have the students cut the shape of a house (rectangle bottom, triangle top, sort of like an arrow) out of the dough than to mess with different shapes of cookie cutters and having to share them; a house shape would also give them a little more decorating space than a regular-sized cutout cookie.

Don't use buttercream or any other frosting to decorate--the decorations won't survive the trip home. Use royal icing to "glue" gummy candies, pieces of candy cane, SweeTARTS, gumdrops, cinnamon red hots, Necco wafers, and other similar candies to the cookies. You could also use alphabet pasta or other pasta shapes, pretzels, Triscuits (for thatched roofs), and cereals such as Froot Loops. Don't use M&Ms, Skittles or other candies that bleed easily when they get wet.

Put the cookie on a styrofoam plate or a well-washed styrofoam meat tray (this makes it easier to set the cookie aside for drying and to transport the cookie home). Give each child about a quarter cup of royal icing in a yogurt cup; use popsicle sticks as applicators. When it's time to go home, slip the plated cookie into a plastic bag.

Royal Icing: Mix 2 large egg whites from pasteurized eggs, 2 teaspoons lemon juice or water (or 1 teaspoon clear vanilla and 1 teaspoon water) and 3 cups confectioners (powdered or icing) sugar. Beat until whippy but thick--this could take a few minutes. Thin with water to desired consistency, but the more water added, the harder it is to control the application and the longer it takes to dry. Because you're dealing with other people's children, please use only pasteurized eggs or meringue powder from Wilton, available at Michael's, JoAnn Fabrics and Walmart.

I think most recipes are probably similar, but the trick when making sugar cookies with kids is the time they usually take to chill. Once you put the dough in the fridge to chill the activity is usually over and you've moved on (unless you do it like a tv cooking show with dough already chilled and ready to go). So I've made "no chill" sugar cookies with my 3-yr-old that worked great. Something like this:

http://www.food.com/recipe/easy-no-chill-sugar-cookies-286900

I can't remember if this is the one I've used, but if not, it's similar.

As for decorating, kindergarteners are probably more able than my little guy, but we've mainly done sprinkles before they went in the oven and colored frosting after they came out. One recipe I really like is adding a bit of green food coloring to the cookie dough, cutting out tree shapes, and then dipping them in white chocolate at an angle after they come out of the oven to simulate snow.