Squats and lunges are good for strengthening your legs, but I also have a more unusual "exercise" you might try. Find a rail or fence, preferably horse height or higher, and use it to practice bouncing and pulling yourself up with your *arms* then swing your leg over like you're mounting. Pay close attention to your knees - if you knee the fence or swing your knees under the rail you're gonna knee your horse. Practice until you can pull yourself up with your arms and keep your knees straight. When you actually mount your horse, don't grab the front of the saddle. Take a handful of mane just in front of the saddle then place your palm on the front of his withers. Place your other hand on the back of the saddle. Your hands should mostly balance you as you pull yourself up so you don't pull on your horse's mane, but grabbing mane instead of the front of the saddle will prevent you from twisting the saddle.
Notice that this technique does not involve using the stirrup to pull yourself up and most of the work is actually done by your arms. If you need to strengthen your arms, try two different types of push-ups. To strengthen your shoulders, do push-ups with your hands spread wide so when you lower your body your elbows are at a 90 degree angle. To strengthen your triceps (back of your arms), do push-ups while sitting up with your arms behind you and your hands facing forward. You can either place of hands on the ground or on the edge of a chair.
Pulling yourself up with your arms works both from the ground or a mounting block. Being shy of 5 ft tall, I find many mounting blocks aren't quite tall enough for me anyway. And I usually ride bareback, so using a stirrup to pull myself up isn't an option. Just remember to be careful not to knee your horse in the side when you bounce.