Many of the Mongolian tour operators offer horse riding tours or have tours that at least include some horse riding. Horses tend to be smaller here than in Europe and the techniques to riding are somewhat different. Firstly, the horses tend to run rather than trot or canter and the rider remains upright with their legs almost straight. You'll soon find out why though when you see the saddles. They're wooden and provide little comfort.
Local nomads are often willing to allow foreigners to hire their horses for short periods of time.
Take care if you're not an experienced rider. The best time to go riding is from June to September when the horses have recovered from the winter. The Gobi is the ideal place to try your luck with camel trekking. Week long tours are now available through some of our Mongolian Tour Operators. The nomads will often be happy to let you sit up on the camels and go a short distance.