In real life, a snowstorm has depth. It engulfs things. We can simulate this by adding several layers, increasing or decreasing the scale of each to make it look closer or farther away. I used five layers of snow. You can have more or less, but five was fine for this image. There may be (probably is) a better/quicker/easier way to do this, but I'm going to stick with what worked for me:
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