So, have solved the issue...
The problem was, that I has set a global variable to true if an object has an texture and to false, if no one was present.
If the last exported mesh has also no texture, the variable was false and no texture was written in the mtl-file.
I have remove that check and now it works...
The checked texture in the image I have used, because the imagefile was missing in your scene.
In the zip is a version for 2010+ 64bit. It´s only a dll. Please remove the one from the addon folder with this one.
If you need an other version, tell it.
This version is still work in progress. But I think you don´t need ICE-Strands to export.
face