I'm seeing some small flakes between the camera and the ground features but I'd expect to see more. What I usually do is set my cloud layer to the same height as my camera and add whatever thickness is required for it to meet the ground. Next, I open the settings panel and its shader preview window(zoom in to a really close view) for the snow fractal, set all scales to 0.01 and then move to the colour tab. Colour contrast of 1 or 2 is good and then I lower the colour offset incrementally. You'll see the shader preview update and when it looks like it's a nice flat plane with the right coverage, I think it should be fine when applied to the snow layer, some minor adjustment is still usually needed but that's the basis of how I'd normally do it.
Try this clipfile, for a cloud layer with a density fractal like this shader preview image.
[attachimg=#]
Make the localised coordinates the same as your camera's coordinates and you can adjust the limits of the snow with the size of the localised cloud radius, you won't want it to go way into the distance since it's all around the camera anyway and that would just increase render time when you don't need to, usually, a small ball of snow round the camera gives a good, fast result.