I've used beets to color frosting for my girls' b-day cakes. I just take a raw beet and peel it and chop it in about 2 inch chunks. Then I just dump the chunks in the frosting and stir around until the desired color and then fish the chunks back out. I imagine it might work the same way with playdough, but I've not tried it. If you're using a cooked recipe you might want to experiment with adding the beets before cooking and afterward. I don't know if cooking would alter the color. (I tried making a beet cake once like carrot cake, but the color didn't show up.)
I think turmeric would give you a nice mustardy yellow, but it does have a bit of a smell/taste used in larger quantities.
You might be able to use chlorophyll or spinach juice for green. I was going to try that with the frosting this year, but didn't get around to it. I was just going to let some frozen spinach thaw and then squeeze it to get the green water/juice.
Cocoa powder would give you a yummy smelling brown.
I think boiled purple cabbage can give you blue—at least I've read it can with Easter eggs. Never tried it.
hth
