Hi, I'm an equestrian too. I used to ride 2 times/week in lessons until I had mono and could not ride anymore. To make your workouts harder for you and not for the horse, you can use exercises while riding. Posting without stirrups is extremely good workout. You can do it both at walk and trot. Staying in two-point position with and without stirrups is also very good exercise, and you can do it as your horse walks and stretches down for either warmup or cool-down. I don't know what riding discipline you participate in, but I know when I started doing dressage, each lesson drained me out completely, because you are not only working to keep your balance as the horse moves, you also give an aid to your horse with almost every step! I also don't know how well you can keep your balance on the horse, and if you've never done no-stirrup work before, start slowly, few strides at a time, and then build up to minutes in a row.
Horse riding is a sport that requires a lot of stamina, balance and strenth, and people don't realise how draining and tiring riding can be. When I'm on a horse, I never feel the fatigue, but as soon as I get off all the muscles in my body are tingling!
To comment on weight loss part, despite horse riding being such a good work out, 2 hrs a week is really not enough to be loosing weight. According to new USDA guidelines, you need to be active 90 min/day to see weightloss. With time it takes to groom/tack/untack/rub down and cool off your horse, you're probably moving around 4-5 hrs a week. But you need to move 10 hrs in order to actually start loosing from work out only. So, I would recommend working on cutting out 100 to 200 cal/day or increasing riding to 3 times/wk.
As a personal example, I've gained 15 lbs in 1 year while riding 2 times/wk in lessons AND spending 8 hrs a day every Saturday mucking stalls, feeding and watering horses, all because I had been overeating about 200-300 calories a day. Even with hard exersize and activity, if what you're eating is more then you're burning, you're not going to loose weight.
Best of luck, enjoy your horse!