K.H.
I don't use icing, I use sprinkles and dyed white sugar and decorate them before they're baked. I also use cookie sheets with no sides so I can tilt them and have some of the extra sprinkles come off before they go in the oven. My 4 yo has a heavy hand with the sprinkles. I also use raisins, craisins, chocolate chips, broken candy canes, anything I can think of as long as it's small. When the kids get older, I may try icing in decorator bags (so they can just pipe it on) and see how they do.
As for cookies, you could get a hand or turkey shaped cookie cutter. I'm thinking candy corn beaks, red hot heart waddles (or licorice), and multi-colored sprinkles for the tail feathers. I also saw some cute cupcakes at a bake sale - white frosting with candy corn tail feathers and beak and mini m&m eyes or something like that. Very cute!