How can I overlay snow onto a static scene to make an animation? I have a scene consisting of a castle in the mountains.  I want to add snowfall to the scene using a particle emitter to make the scene animated.  That's the easy part.
My scene takes quite a long time to render so as the only thing that is changing is the snow, I would like to avoid rendering the entire scene for each frame.
I tried creating a new blend file with the rendered scene as an a flat image, and adding the snow, but it looks exactly like that - snow falling in front of a picture.  

I'd really like the snow to look as if it's falling into the depth of the scene.  I suspect this might be possible by some clever compositing trick or rendering the snow and the scene separately in different layers, but my Blender skills aren't quite up to those kinds of tricks as yet.

Can anyone guide me to a tutorial (or explain how it might be done here if it's that simple)?
Once that's done, I need to work out how to loop the snow so that it doesn't jump when it loops around, but that can wait for a separate question.

I'm working in 2.79 and Cycles.
Some tips that might help: 


If you want visual depth, then some snow has to "dissapear" behind the
castle (So the snow density in front of the castle is much lower). 
If i understand your current setup correctly this doesn't happen.
If you put the snow and the castle on different layers be sure to
tick mask for the castle layer on the snow layer (https://docs.blender.org/manual/en/latest/render/post_process/layers.html)
Also make sure your particle emitter Geometry has enough depth.
(horizontal plane).
Then it might be nice to add some force fields (to add some vortices
etc. you might add keyframes to the strength of some force fields and
use noise
How to make flickering light?
...


PS: You can loop your particles like this: https://m.youtube.com/watch?v=yanQ1C7GB04