There's several companies that offer horseback riding in the Metro Phoenix area, but I chose one which had a good presence on the internet, good reviews and quick to answer on the phone bacaue I reserved the day before we went on April 2, 2013.
I found http://www.arizona-horses.com/ which is actually Pondersa Stables which is based on South Mountain and has been in operation since 1970's. As said in other reviews, the guy Danny who answered my phone call was very easy to talk with, specially to a beginner like me who wanted to bring twin 9 year olds on the trail, haha. They do have pony rides for younger kids, but I opted for the one hour trail ride which would be their easiest trail but still give a good view of the mountains and desert.
They also have two or three hour rides, and they will have a guide that will suit your activity level. They have you sign a "waiver" for injuries (which is standard with this kind of activity) and also it is a way for them to assess which level you are i your horseback riding skills.
We chose the 5 PM slot, but as in other review, the actual trail actually starts a little later because they have to organize all the people who will be riding at the time. The cowboy guides are "guides" and will not be like smiling tourist guides, but real cowboys who really look at how you are on the horses and how the horses are behaving. So, don't expect them to be talking much to you unless you are in a small group. Our group had about 15 people and we were told to be 3 ft away from each other - the kids are at the start of the line and the parents follow after them. So, it was odd that we were too far away from our kids but I still got some pictures of them from the distance.
They also offer dinner steak or breakfast riding tours, but we did not do those yet. The one hour trail was exhilirating and it was fun hanging out at the stable office before we start our trail because you can pet the horses who seem to be used to all the many people they meet each day. Just be careful about standing outside the stable office area, behind the horses..horses might kick and cowboys are keen on making sure you stay in the designated waiting areas.
Overall, a fun experience and a great way to experience the southwest. I made a video of our trip and hope you enjoy this (on youtube):