My Jesse was doing the same thing, I recently brought him to the vet
and found out that it is an allergy, his skin is affected by it. all around his schnout & forhead. Vet thinks it could've come from thistle weed found in
tall grass. I have Jesse on anitbiotics & prednisone for the discomfort. He doesn't grind his face in the carpet that much ever since being on the medicine. and I have noticed a difference.
However, Jesse does wipe his face into the carpet after eating too possibly to clean his face off if hair is long, and after bath to dry it...