You need to determine the empty weight of your horse trailer first of all. If its less than 7 or 8k loaded with horse and gear you should be fine with any 1/2 ton gas truck. Closer you get to 10k the more I would lean toward a 2500, either gas or diesel. What people often forget is that a 2500 chassis is not just more pulling power via motor, but stronger frame, bigger springs/ more robust suspension, and most importantly larger and better brakes. Stopping the load is as important if not more important than dragging it.
I'm not a big proponent of gas 2500 DDs though, because as a DD you're then dragging around all that stronger HEAVY duty chassis which uses more fuel when unloaded. A lot of 1/2 ton trucks can be optioned to tow 10k now, but its not a real comfortable experience at that capacity.