The short answer: T100s are rated around 5,000 lbs regardless of drivetrain. You really want the 3.4 engine - it is the most powerful and still barely powerful enough. Manual transmission would be preferable if you can handle driving one.
You ABSOLUTELY need a class three hitch. UHaul or similar should be able to provide you with one and install it for less than $300US. I personally bought my own for $150 and installed it myself. You also ABSOLUTELY need an electric brake controller (I recommend a Tekonsha Prodigy P3 - best compromise on price & quality).
Have you towed horses a lot before? If the answer is no, then you really need a heavier vehicle to learn on. The T100 is a very light, underpowered truck, and although it is definitely up to the job, the closer the weight of your vehicle is to that of the trailer the less forgiving the setup will be. If your heart is set on a Toyota, a 2000+ Tundra would be a very good choice, especially with a V8. Even a v6 tundra with the same engine would probably be better than a T100 by virtue of weight and a longer wheelbase. I have personally towed about 10,000 miles with a 2000 v8 Tundra and much prefered it.
I do not know the technical towing capacity of the 4runner or truck for those vintages, but I would consider towing with either vehicle VERY UNSAFE. The "truck" is 9 inches narrower in track and has a shorter wheelbase than the T100. I believe the 4runner is also narrower and has a shorter wheelbase. Both of these factors would make these vehicles significantly less safe to tow with, regardless of curb weight or tow rating.
Anyway, if after all of this jibber jabber you are interested in towing with the t100, you will need to address the tongue weight, either by supplementing the truck's suspension with an additional leaf, active link, etc., or you will need to get a weight distributing hitch. If you have a very light trailer, this may be a non issue.
What kind of trailer do you have and what kind of horses? My wife and I at one time had four but are presently down to one, a dutch warmblood / belgian cross... presently 16-2 and 1,300lbs. Our trailer is a kingston steel frame, aluminum skin 2 horse (standard width, no tack room). It weighs 2,700 lbs. You can get yours weighed at any feed store with a scale.
Here's my setup with a thoroughbred we no longer have:
More Q's? just ask.
P.S., I do have a tranny cooler. Should be no more than $150 parts & labor.