This sounds less like a balance issue to me and more like a confidence issue. To make it worse it is a self fulfilling prophecy... Get a little off, grab horn, and throw yourself really off. Yup, that's right, grabbing onto that horn actually puts you in a WORSE position as far as balance and seat are concerned. It's a mental crutch that makes you more likely to come off by throwing you out of position and encouraging to rock forward out of the "pocket" of your saddle instead of sitting deep, relaxing, and riding through it.
If you absolutely must use your horn you should push against it with the palm of your hand on the backside of the horn, forcing your body down and back into the sweet spot in your saddle and forcing yourself back onto your tailbone.
The best solution is to forget the horn is there. It's to tie a rope off to, not keep you on the horse ;)
Just practice and gain confidence. Avoid the horn ;) If you can convince yourself to leave the horn alone a few times you'll probably find you can get through a stumble or lapse in your balance better without it and be just fine. You can do some stuff in the arena, such as working with no hands and even with your eyes closed on a lungeline or riding bareback/no stirrups/in an english saddle.