Is there a way to render just the snowflakes off, then reapply that render to the animation for a final pass?
The issue there may be intersections/pass throughs if you have the particles dieing on impact.
If that is the case you *could* set all your objects to transparent (perhaps not an easy task) and then render the particles pass that way.
If you aren't concerned with passthroughs you could save two copies of your Project file. One with everything but the particles turned off. The other with only the particles turned off.
There are a lot of different ways you can do this... but since time is of the essence I won't suggest things that have a higher learning curve.
Okay, I lie. You could render the scene (to image sequence!) and generate the snow in a program like Blackmagic Fusion.
Import the sequence into Fusion and your scene will appear to be in front or behind the snow depending on where you place your images.
Render different parts of the scene and place those images where you want them.
Or... do the same thing in A:M!
Render out as many elements as separate passes (will significantly lower the hit on memory)... then bring all the images back into A:M as Layers.
You could run a pass of the particles separately and bring that in too or render the particles live along with the Layers.
Too much info right?
Email me the project file as I have a lot of time on my hands at the moment and I'll render and composite it together for you.