A bit of everything was worn depending upon season and region in Italy. Summer months in the southern end, tropical uniforms were the norm. Cooler months further up the boot, wool was in use. Regardless, you can't go wrong with wool on your army. Wool great coats were issued when inducted so they too were worn. The German army operated no different than any others, as items were not needed and impaired unit mobility, they were collected and stored at the company or higher level and redistributed as ordered.
The most commonly available camouflage clothing item period, was the shelter quarter. While prestigious or favored units recieved factory made clothing, the zeltbahn was always available to everyone. Keep in mind that wearing one for camouflage reduces mobility, hampers access to equipment, and increases body heat. All of these drawbacks could theoretically explain why it is seldomn seen in photos.