I am going to say you need a full size truck for that load. Horse and trailer would undoubtedly be over 3000lbs, which is not going to pull well on a midsize SUV. Possible, yes, smart for more than "once a year" towing? I would not recommend it.
I would recommend a full size truck/ framed SUV with a V8.
We used to pull a 3000lb boat with our little S10 blazer (4.3 vortec), and it was sketchy and underpowered to drag up hills. Also it was a handful to stop.