As with most things of the hickory era there are few written records of the history of the golf grip. It is unlikely that the shepherds who, if we believe the story, turned their crooks upside down to hit stones on the hillsides, would have wrapped anything around their "clubs" to get a better grip.
It is unclear when the first grips appeared on golf clubs, but generally speaking wool listing was used in the 18th century, this was then covered with sheepskin in the 19th century, and leather and rubber were used in the 20th century. However, as with the change from the featherie ball to the rubber core ball, and the change from the hickory shafted club to the steel shafted club, it is clear that there would have been considerable periods of overlap as the different styles changed.
No doubt, if you have experience of hickory clubs, you will have seen grip "tide marks" where grips have been replaced through use and wear, so it is clear that a club cannot be dated merely by its grip.
Golf grips, as well as the wool listing, sheepskin, leather and rubber have also been made from different fabrics, ceramic, gutta percha and cork.
The clubs above show examples of the circular with flattened front, square, fluted, ringed and Thumb groove grips
As with golfers who used to apply French chalk to the faces of their drivers and brassies to prevent the ball skidding off the face, so golfers applied various treatments to the grips of clubs, including, olive oil, wax, pitch and varnish, to obtain a better grip.