I have been looking at and testing various weather/texture mods and they are all awesome but they all seem to ruin the feel of morrowind by making it sunny and bright. I see morrowind as being a beautifully dark and dreary place, very foggy and grey. Are there any mods that better the weather while retaining the dark and dreariness? Perhaps making it even more so?

Do you have MGE installed?

I installed a pack (that I most likely cannot mention here) that included MGE. Though I only followed instructions, are there MGE settings to increase grayness and fog?

You can tweak your ini in many different ways to make the game feel darker and less sunny.
You could also increase the chance of rain/cloud/etc in any region that you want. (in the CS)

MGE also allows the usage of shaders/blooms to change how the game is visually displayed. experiment with them.
All MGE question should be posted in the current MGE thread.

Yes.

I was not aware of this. Thank you very much.

Think you should be able to edit the RGB settings of the fog in your morrowind.ini. Lower values means darker fog. Same goes for overall weather, I've set it so night is nearly pitch black which does wonders for immersion.

You could try the darker morrowind texture packs which sound exactly what you are looking for. Colors are darker, building textures are sort of crumbly, etc.