It should be a simple process, the same as when we make styrofoam troughs that need to weather outside the entire year for many years:
1. Shape your styroboulder
2. Use a heat gun to melt and fuse the styrofoam "balls" together and make the surface firm and paintable.
3. Paint as desired with a weather durable paint. Use a flat sheen, as opposed to glossy.
Some ideas: