If you can find one with a well detailed color channel, it might help a little.
Don’t expect miracles by changing the snow material though. If you look at images of real mountains under cloudy or night time conditions, you will see the snow itself is a rather solid white. Most of the visual detail happens because there are very detailed patches of rock poking through the snow.
Example:
The only texture in this render is a single noise to make the transition between snow and rock a bit more detailed.
The snow is a solid white and the rock a solid brown, no textures used. The visual complexity is created entirely by the complex transition between the two materials, which I think is the key for good looking mountains. I purposefully took this image under the flattest lighting possible and it holds up pretty well.
Here is the scene for that test render if you wanted to take a look.
mountains_snow.blend (2.5 MB)
From the images you posted, I think it’s the polygon count. Your mountains add up to 15 millions triangles in the viewport. I can imagine this would be a problem. Disable the viewport levels on the subdiv modifiers and it should greatly reduce the problem, at least in the viewport.
For the render, there are 2 things you could do. Are there some mountains that are far away and need less detail? If there are, you can remove the subdivision modifiers on those to save performance.
For the closer mountains, make sure they are all using adaptive subdivision, not just some of them. It’s not just for micro-displacements, it’s also for performance, but you have to set a good dicing rate to get the benefit over regular subdivision.
I notice you have a displacement plugged in the material, but it’s set to “bump only”, which means your displacement isn’t being used as actual displacement, it acts like a bump node.

If you are fine with this, you can set the adaptive subdivision’s dicing scale to 3 or 4. It will have much better performance and is still good enough for a model without displacement.