For purposes of carpooling since the entrance fee is $7/vehicle with up to 4 people. You can get in for free if you have a State Park Pass. Meet at the parking lot for the Ball field that is on N 10th St in Cottonwood, note that this is right on the way to the park entrance. Below is a map which shows both Dead Horse Ranch and the meet up location.
Directions coming from Cornville Rd.
Take Cornville Rd and go across 89A to Mingus
Turn Right onto N Main Street in Cottonwood
Turn Right onto N Tenth St.
From the parking lot on N Tenth St. you can continue on N Tenth St to reach the entrance to Dead Horse Ranch State Park