I would not get a small pickup for trailering a horse.
The weight of the trailer alone, would put a strain on a smaller truck I would think.
I have a 2 horse Sundowner, G/N, with tack room. I pull it with a 98 Chevy 2500 series truck. It pulls the horses fine.
I don't show, or go much. If I had of been planning that, would have maybe gotten a fancier truck but don't need one for what I do.
You might check out HorseClicks - Horses for Sale - FREE Ads
, and look through all of their ads.
Some of the horse magazines have had good articles on what to pull a horse trailer with.
Do take the time to look at a NADA book for vehicle prices, and find a really good mechanic too, before the truck purchase, so that before you buy one? You can take it to him and let him give you his thoughts on the vehicle.
Hope you find something really nice, that fits your budget.