Here is a good site to get all your towing capacities.

https://www.cvpi.com/showroom/rv_trailer_towing/2004/2004_default.asp

I don't know what brand trailer you have. Many three horse trailers are set up so that the center of the two axles is under the shoulder side of the horse. That means with one horse in the center stall, very little additional weight is added to the hitch.

On a gooseneck trailer, because of its relatively heavy hitch weight, you can carry a horse behind the axle without causing any tracking problems. You will only slightly unweight the hitch, which if I read you correctly, would be to your advantage.

Carrying two horses, one in the center stall and one in the rear most stall should not adversely effect your hitch weight, and would not cause any tracking or trailering problems.

We consistently load like this and use the front stall to carry hay, tack boxes and an electric bicycle.

Gard

There are several factors here...  do you have an 8' bed; that is, the long frame or a short frame F250? Reg cab, extended cab, crew cab? 

Do you have 4WD or 2WD? Is it the 5.4l or the diesel?

3700 tongue weight is more than 30%... that is very scary. What's the gross vehicle weight rating of the trailer? Sounds like way too much cabinetry in the LQ / front end of the trailer.

A simple check would be to hook everything up, then measure how high from the ground the back bumper of the truck is. Load up the horses and measure again. If the bumper goes UP, then you are removing weight from the hitch; if it goes down, then you're adding weight to the hitch.