I have been having some problems with various texture mods. Many that I have tried to install (Qarl's Bottle Replacer, Alan’s stilt strider retexture, Better Books) refuse to work. I followed the instructions precisely as directed and tried extracting with both 7zip and Winrar. I can see the files in their proper locations in the Data Files folder, yet they won't show up ingame.

Even more strange is that I have a few other texture mods installed that work fine (Better heads, Better bodies, a few others). I have also installed a few other mods (Misc Items Replacer, Darknut’s Creature Textures, Sharpened Models Weapon Replacer) but as this is my first Morrowind playthrough I can't tell whether or not they are working.

Has anyone encountered similar problems?

Are you using the Steam version?

Yes, could that be the problem?

Yes.
You will have to redate the BSAs to what the original ones were to make some texture replacers and mesh replacers to work. http://code.google.com/p/mlox/wiki/Tes3cmd has a nifty little command to redate both the BSAs and the ESMs to their retail dates. Simple to use.

And as a side note: If you're using Vista or Windows7, make sure to install Steam outside of your Program Files folder (e.g. C:\Steam\etc ), that way you avoid access issues with Morrowind, especially when modded.

Ok, I installed Tes3cmd but I'm not really sure where to go from here. The instructions in the link say to

"...use "cd" to change directory to your "Data Files" (or wherever you want to work on your plugins), and then use tes3cmd there."

What do they mean by this?

Also, will I have to reinstall any mods?

Okay, to explain this a little better:

You need to have tes3cmd installed in the Data Files folder (we will do this since it will make you life a little easier here)
Then, run the Command Prompt (Start -> Run -> cmd) - if you don't see the Run option in the start menu, then hit the Windows Key+R to open it, and type cmd as before
From here, you need to use the http://en.wikipedia.org/wiki/Chdir (change directory) to get to the Data Files folder
Then just type "tes3cmd resetdates" and you should be good to go

Oh, and you shouldn't need to reinstall the mods, the redate should square things away so the textures/meshes you installed will be dated more recently than the bsa files, and so they should begin showing in game. Hope that all helps