Spray-painting polystyrene for outdoor use
First of all, using regular spray paint on polystyrene will melt the material, damaging it significantly!

So, before anything else, I'd suggest either coating your polystyrene head, or using a polystyrene-safe spray paint.


To coat the polystyrene object, use gesso (or another acrylic primer), plaster, a polystyrene-safe primer spray paint, or even white glue.
Now you can safely apply the fake stone layer. You can opt for a spray paint that's suitable for outdoor use, or use your current spray paint, and coat it afterwards.
After the recommended amount of drying time, you can protect your creation with, for example, a clear acrylic coating spray.