UUUMMMM, I think it would be ok so long as you go over only small jumps. You have to remember that most western saddles are much bigger and heavier than english saddles. They constrict movement more and can cause other problems for you and your horse. I had a friend that jumped in a western saddle. She had a jump that was too big and her horse got to close to it so when he took off, the saddle horn hit her in the stomach and knocked the air out of her. When I would jump, I generally do it bareback. But, I do have one of those cheapy english saddles for when I have the desire to ride one (not very often).
I think as long as you don't go to high ur fine. I was jumping in a westren saddle and no stirrups and the horse jumped a 3 ft jump 5 ft no joke. Then when he landed he went to bucking so as long as you don't try that stunt I think ur fine.
I have jumped in a western saddle. In an arena and lots of times on the trail. I just hang on to the front of the saddle or to the horn so as to not stab myself in the gut, I can hold myself up and away from it. Here is a pic but this saddle doesn't actually have a horn on it just a big roll thing at the front which can hurt thighs!
Remember there western saddles out there without horns. McClellan, endurance style, Aussie-western hybrids. I never have cared for a horn on my saddle. Its always in the way, going under tree branches, mounting or dismounting, I just started with a western-aussie hybrid saddle and that's what I like. I also have a endurance saddle with a very high pommel rounded for easy grabbing if needed. If I ever have to work cattle or need to dally a rope to pull downed tree branches I want a horn..
The saddle I ride in now is a Spanish lightweight hornless. Here's a pic. Of Sassyfras with her spanish saddle.