You'll get those suggesting a 1/2 ton but for towing livestock I wouldn't go with anything less than a 3/4 ton pickup. While the 1/2 tons might be "rated" to tow heavier loads they are not as capable of it as a heavier rig. For me, when it comes to horses, the last thing I want is broke down and possibly wrecked because I went with a lighter duty pickup. If it was just a travel trailer I wouldn't hesitate using a 1/2 ton.
Things to look for, I'll go from the assumption you know nothing about what is needed as that's easier. Ignore anything you already know:
-For automatics, look for one that has a tow mode and use it when towing. If manual, don't lug it to much and don't over wind it for to long.
-Transmission cooler, should come with tow package but you need to look.
-Trailer hitch, no towing from the bumper.
-Trailer brake module.
-Tires that are rated for the maximum weight of your pickup. That's pretty easy to find, open the door and there should be a sticker there with GVW listed. At a minimum you want all 4 tires able to support the GVW when added together. But (always a but) that's at maximum air pressure in your tire. Most of us don't run with maximum pressure so you'll want more tire than that. As an example, if your GVW is 10,000 pounds then at a minimum you want each tire to be rated for 2500 pounds (at maximum air pressure). Personally I would go 3500 for plenty of safety margin.
-If it's a used pickup, get it checked out by a mechanic.
-Diesel gets better fuel mileage and has more torque for towing. Gas is cheaper than diesel.
-When it comes to towing, torque is your friend and more important than the HP figure. Ideally you want a lot of torque low down in the RPM range which you'll get from diesels and most big block gas motors. Problem is big block gas motors are not known for their fuel mileage!
-Gearing is important. High gears (low numerically like 3.23's) get you better fuel mileage but don't tow well. Low gears (high numerically like 4.10's) do better towing but hurt mileage. Unfortunately I can't tell you what gears to get because that depends on the vehicle type, engine, tires and intended use.
-2x vs. 4x. 2 wheel drives are cheaper to buy, cheaper to operate and easier on gas. 4 wheel drives give you the ability to crawl in and out of pastures, gear down for rough ground and of course help in slick conditions. Which to get really depends on your situation and personal preference. Just something to consider, 4x do cost more up front to buy but you'll usually get that back when you sell it so your cost really has more to do with upkeep and fuel.
That's all for now.