You have more options than simply a "Western" or "English" saddle.
Personally, I don't care for saddle horns, especially when it comes to trail riding. The horn just seems to be in the way.
You could consider an Australian stock saddle. Some are built with a horn, others without. They were designed for long hours of riding, and to hold their rider in the saddle over a variety of terrain.
Or, a simple endurance saddle. I have one that is referred to as a "western" endurance style, in that the overall structure is similar to what you'd find in a typical western saddle, with a round skirt. However, it does not have a horn. There are also endurance saddles made more like an English saddle.
Many online tack stores have demo programs for their saddles so that you can find one that works well for you and fits your horse. A local tack shop might also have used saddles on consignment, and they may allow you to test-ride one, or at least take it to the barn to see how it fits your horse.