In my experience this is a case of the textures just not loading properly or not at all. 98% of the time, the problem will be local and most likely a hardware problem, especially if you are certain that the files and mapping are set up correctly.
For me, personally, it tends to be caused by graphics card failure. This might not be the problem in your case, but when the graphics card in my older computer would overheat is when textures suddenly started appearing as blobs of white. I remember way back when, my computer would start getting pretty hot and then I'd load onto a map and see white cows and NPCs with white heads everywhere, and the problem is non-existent on a computer with a newer/faster graphics card or more cooling.
Of course, that's only how it went down for me. It might be something entirely different for you :)
I'd suggest trying to play on another machine with either better cooling or a faster graphics card - at least that way it'd be easier to tell if the problem is local to your computer or an error with the files.