Dead Horse Point gets it's name from dead horses. It is easy to put up a fence of about 30 yards at the neck of the Point which is a peninsula attached to the mesa. Then you can graze horses on the peninsula and not worry about them getting away. There is only one wrinkle, no water. Periodically the horses had to be taken off the mesa and hydrated. According to legend of which there are several versions some cowboys or rustlers put some horses at the Point intending to return before the lack of water became critical. They were delayed and when they finally returned all the horses had died from the lack of water. Dead Horse Point had nice campsites with no water and 20 amp electric under the table.
Dead Horse Point State Park also had incredible Sunrises, unfortunately my digital pictures don't do it justice.
The Park also overlooks some Potash Mines which are interesting. They
used to have miners mining the Potash which is used as fertilizer. One
day the Colorado River, like the Saddle River flooded its banks and water
when down into the mines. While in the mines it dissolved the potash and
when pumped out the water dried in the sun and there was the potash
for the collecting. So now no more miners just water pumped into and out
of the mines and allowed to dry in the desert sun before it is harvested.
Canyonlands National Park also has arches, some with spectacular views of the canyons below.
There are of course other places to view the canyon below the rim.
That's about as close to the edge as I wanted to get although one of the
NP Rangers stood right at the edge while he described the park to us.
From Canyonlands we headed SouthWest to Capitol Reef National Park