I've created following scene:
What you see is the light shining through a window to the back wall of the room. Outside is a tree blowing in the wind. What I'm trying to simulate it a stormy weather, so I need to add rain to the scenery as well. However, I just need it as a shadow through the window. How is this done, can it simply be done through Unity's Particle System, or do I need shader etc.?
Use particle system, it has Renderer Module where you can play around with material/texture/shader to get the desired result.
I would go for a grey/black colour to make it look like a shadow