Recently we realized that we have egg on our house....yes, egg! We think the eggs must've been thrown on Halloween. We didn't notice until now because we just removed a window air conditioning unit over the weekend. The a/c unit shaded the part of the house that got hit with the eggs. We have a stucco house with wooden trim. We scrubbed the egg off of the stucco easy enough, but the egg is not coming off the painted wood very well. Our house hasn't been painted in many years and is faded and peeling. That opens up pores in the wood where the paint doesn't completely cover. I think it's futile to try to scrub it off any further. We'll probably have to sand and repaint around the window in this case. It's not fair though! We gave out really good candy this year! 
That's sad that anyone would throw eggs at your home for any reason, but it sounds like the house is due for a bit of TLC any way, since the paint is faded and peeling. Sanding and repainting sounds like the best solution. Perhaps it's because you gave out good candy to the younger children that the older children got jealous and threw the eggs. We don't get any visitors for Halloween where we live, so you're lucky you get to see all the little ones dressed up for Halloween.