F150 f 250, doesnt have anythign to do with power, it has to do with how much weight the bed of the truck can hold. My F150 has a bigger more powerful engine and a higher towing capacity than a gasoline powered F250.
Lots of features on the truck effect the towing capacity.
search FORD Towing guide, for the year truck you are looking at.
You must know the engine, (you already said 4X4) and rear end. Usually a code on the door panel, also if the truck has the tow package installed. Basically a heavy duty radiator and probably an oil cooler. Pretty much all recent F 150's with the 5.4 engine has the added cooling capacity.
An F150 with a 5.4 engine and anythign but the 3.31 rear end would have no problem with a bumper pull or aluminum goosneck 2 horse trailer.
A simple steel bumper pull with a manger tack area will weigh about 2800 lbs at the most. Add 2 horses and some tack and you are still under 6000 lbs.
Not really a problem, however get a f150 with 3:31 highway gears and a 4.6 engine and it wont get out of its own way. BIgger liters on the engine and bigger numbers on the engine and bigger numbers on the rear end is always better.
Go here, https://www.fleet.ford.com/showroom/...06_default.asp
punch in the year and scroll down to towing. It will give you the weight limit. Stay well below that limit and you will be fine. I imagine Chevy and dodge have something similar.
You want specific ? Ok look for a F150 or F250 with a 5.4 liter or larger engine and a 3.73 or 4.10 rearend made between 2004 and today. For a basic 2 horse bumper pull.