From the commentor KCMORon on http://www.shorpy.com/node/8316?size=_original : It's my speculation that the covers were more than just variations of tread design, they were an extra layer pf protection from sharp rocks (no pavement) and the frequent flats were a fact of life, that's why there were 2 spare tires
They appear to be "Billet" detachable tire protectors with "contre envelope" attachments or similar. ("The Horseless Age" Volume 15, January 4, 1905)
The "tread" part has flaps which extend over the sidewall on both sides and hold a wire extending around the circumference and fasten (tighten) in two places with a screw and nut.
At that time here were many types of tire protectors of various designs and attachment schemes. Some also claimed to improve traction.
It's my speculation that the covers were more than just variations of tread design, they were an extra layer pf protection from sharp rocks (no pavement) and the frequent flats were a fact of life, that's why there were 2 spare tires