Studded tires aren't generally used, or legal in California. Not enough to affect pavement wear.
(Added: I looked this up, it seems there are some allowable conditions:
Vehicle Code - Tires )
But the CHP cruisers up on the summit use them.
That wear is from truck traffic. And especially from the mandatory tire chains on trucks, required during times when a truck that can't get traction turns the entire freeway into a parking lot. There were posts over on the 'towing something wrong' thread showing a CHP cruiser tugboating, pushing, a loaded semi that hadn't chained up, to get it moving again uphill over the summit.
That's one of the heaviest snowfall regions in the US. One year a train got stranded in overwhelming snow near what is now the freeway.
I'm very familiar with Donner pass, I've driven it hundreds of time. When I was a kid I worked one summer at Donner Lake and often hiked up to an overlook to watch the construction of that miles-long grade that comes down from the summit past Donner Lake. 'Earthmoving' there was absolutely brutal. Every day there was blasting of extremely hard granite, material at the peak of the Sierras that had resisted erosion better than anything else in the region. Then awful screeches as bulldozers and belly-dumps gathered up the blasted granite for fill farther down the hill. The wear on that equipment must have been severe.