With a little help from Google, I discovered several suggestions for making colored icing without artificial food coloring. You can't get as bright of colors using food sources for coloring, but I was still pretty happy with the results.
One my of my strategies was to make snow flakes that wouldn't need color. I sprinkled some sugar on the the wet icing to give them a little shine.
The lavendar color is from blueberry juice - I just put some frozen blueberries in the microwave for 10 seconds or so and used the juice that came out, run through a sieve since blueberry seeds are small.
The raspberry color is from frozen cherries (similar process as for blueberries, but no worry about seeds).
I made a pale pink using beets. That was a more elaborate project that involved boiling beets ahead of time.
And the orange on the star is from using tumeric. I read to use stale tumeric, but mine wasn't old enough so it did impart some of the flavor to the icing. I also experimented with cinammon for brown, but brown icing was kind of weird.
I heard that pomegranate juice would make a good pink, but I was too cheap to buy expensive pomegranate juice and instead bought a pomegranate. But the color was too pale to affect the color of the icing much. I also tried using orange juice instead of (soy) milk in the icing to achieve a pale orange, but it came out looking about the same as the soy milk icing.
For decorations, I used granulated sugar, dried fruit (blueberries, cranberries, yellow raisens) and some chocolate covered sunflower seeds from Trader Joe's. They are colored with natural food coloring (using things like beets, tumeric, spinach juice). I might try some of the health food stores next time to see if they have some kind of sprinkles that use natural colorings.