I know of two places in
Arizona which will suit your needs. There is a working cattle ranch called Grapevine Canyon Ranch, it might be worth your while contacting them. They do offer accommodation and rides around the ranch, but they also have several other activities for example:-
Join us on a pack trip in the rugged Dragoon Mountains, once home to the fierce Chiricahua Apache. After a day's ride through their old camping and hunting grounds, we set up our camp in a picturesque canyon, then enjoy a dinner of steak, beans, and all the fixin's cooked over a campfire. Later, we relax under the twinkling stars and listen to the lonely howl of a coyote, the sounds of the horses jostling each other on the picket line.
In the morning, the smell of cowboy coffee and sizzling bacon wakes us, ready for another day's adventure.
Price is $100 per person per night out, in addition to the accommodation rate. Minimum fee is $300 plus tax. Call 1.800.245.9202 for availability or more information. Pack Trips must be booked in advance.
You could also try the Williams Family Ranch in Wickenburg where they offer similar trail rides. As well as Round up, working cow trips and a 'Ranch Bar-BQ'