I would think that would depend on where you want to go on vacation. I haven't done it in couple of years, be we rode horses in the San Juan Mtns. (Ouray, CO), in Rocky Mtn. National Park (Estes Park, CO), and in Glacier National Park (Many Glacier, MT). All three are beautiful and wonderful destinations for the family. It was available near the Tetons as well (Yellowstone NP).
I went to Big Ben a couple of years ago and although I didn't ride I think I remember seeing a group out riding (mind starts to go as you get older).
Many parks have outfitters close by who cater to visitors (tourists). Have fun whereever you go. Ouray is a great family vacation spot. About a two day drive from Houston. You can spend the night in Santa Fe and drive through Durango the next day (narrow gauge rail line in Durango if you like riding trains). You can rent a jeep and drive over the mountain passes from Ouray (or ride horses), etc. Ouray is a couple of hours north of Durango. My niece worked for an outfitter group from Gunnison, CO, about two hours north of Ouray. Lovely country. You should give it a try sometime if you have never been.