I hiked Coyote Gulch in 2003 during mid-summer. I used the Red Well trailhead, off of Hole in the Rock Road, as an entrance and exit. I started out early in the morning and walked down canyon all the way to the Escalante River, where I camped overnight. The next morning I hiked back out the same way.
The hike begins in a very dry part of Coyote Gulch. It quickly merges with Dry Fork Coyote Wash and shortly became a walk in water for me. I literally walked in water for about 75 percent of the hike down, and then back. I had planned ahead and brought river sandals along, making the walk easier. Obviously drinking water was not an issue on this hike. Not only was there plenty of it, it poured out of dripping springs along the way. I held my water bottle under the spring, filled it and drank some of the best water ever. My filter never came out of the pack.
There are a number of arches to see along the way. There are also a couple of pit toilets, or there were in 2003, placed in the open, in the middle of the canyon.
I camped at the foot of the trail that leads down from Forty Mile Ridge. From there the Escalante was a muddy few hundred meters walk away. The Escalante River is here considered part of Lake Powell, as the high water mark is up even higher. It was smelly, muddy and nothing much to see at that point.
Mosquitoes were definitely an issue at that time. I had brought along a bug net to sleep under which saved me from being eaten by them.
The 1:24,000 mapsheets for this hike are Big Hollow Wash, King Mesa, and Stevens Canyon South. The Trails Illustrated 1:75,000,
Canyons of the Escalante Trails Illustrated Map
is a great planning map for the area.