Not a picket pin. A reader over at horsetopia.com said this...
Hehehehehe!
I know exactly what this is. It may not be it's intended purpose for which it was originally designed, but I can tell you what it was used for.
After consultation with my 1920's vintage father who immediately identified how he saw this exact device (and other similar designs) being used in the late 20's-early 30's. I've even seen these used as late as the mid-1970's...
First, the arm attached to top of the stake rotates, but will wedge into the ground with the exact intent of making is especially difficult for a horse to pull out of the ground. Enough of the teaser.
The key here is the design of the pulling harness being used by the horse and cross-tree to which the rope is attached. This type of harness was used in practical form for logging, but a dogging chain would have been used instead of a rope to pull a log. But this device, intended or not was largely used as a training device to teach horses to intermittently pull and release and then stop pulling when resistance (the stake pulling free from the ground). "Stake pulling" to simulate pulling stumps was a big event at rural county fairs. Used as a training device, it teaches a pulling horse to slightly rear up, anchor with the hind legs, drop the shoulders and use it's weight in a downward direction to start a pull or exert a sudden forward force. A heavy sledge loaded with a couple of thousand pounds of rocks would be better but less convenient which is why this device is an oddity.
The practical application of this device as a working tool was to be a portable, yet easily removable anchor point for a pulley or for a rope that passes through a pulley. This device was used in logging or to set up a pulley and rope system to facilitate great mechanical advantage (through multiple pulleys and stakes) for dragging or moving extremely heavy objects or loads.