I don't think there is a set number of hours per se. The right answer is what works for your personal situation.But until then, how many hours should they free range minimum?
We allow ours out after first light for a couple of hours until the rising sun soaks the yard and run and then it becomes too hot. They usually self return to the run by then for feed and water and to cool down under the fans. We otherwise leave them confined all day during the heat as the ground is too hot and we have not been blessed with any breezes. We live in suburbia so not in the country where the wind blows freely. We let them out again for the last 2-3 hours before sunset. They self return about 30 minutes before roosting for feed and water and to cool down before entering the coop.
The "coolest" part of our day is early morning (temps around 80-85) and early evening when the temps are still 90+ but we have almost complete shade by then. We still monitor them closely for heat exhaustion and over exertion.
It's unfortunate people let their dogs run off lead on the hiking trail - this is never ok in public spaces in my opinion. They do it at the city park as well where everyone goes to walk, ride bicycles and jog. Some people are inconsiderate and always will be. I hope you have up no trespassing signs all over the edge of your property that runs adjacent to the trail.