I am wondering if I could paint a picture on the Whip n Ice? Could I use the extract to help dry it or would it ruin the icing?

I wouldn't recommend it. If you barely touch it, after it has "crusted" for lack of a better word, it will leave a mark, that no matter what you do, won't smooth out.
I know I tried to smooth out a spot on a whip-n-ice frosted cake, and had to scrape everything off and start over with a new batch of frosting. HTH

On the flavorright.com website under the videos (which are amazing) there is a video that shows a woman decorator painting on the cake using silver dust and lemon extract.