Towing capacity is one number to know. However, how much you can put in the back of the truck bed is another. Combined weight is yet another. There are a lot of people out there who have 3/4 ton trucks pulling large gooseneck living quarter trailers that are still technically overweight. How? They are fine in towing capacity and total combined weight (loaded trailer + weight of truck) but the weight on the hitch (how much to put on the truck bed) - they are over it.
Furthermore, it is very difficult to find numbers from manufacturers like Ford about what is technically your weight limit on the hitch. They also differ between bumper pull and gooseneck. Usually, about 10% of the total loaded trailer weight will rest on the bumper pull hitch and 25-30% on the gooseneck hitch.
For example, let’s say you have a 2H bumper pull trainer that weighs 3200lbs empty (your trailer decal should tell you this). Two horses x 1100lbs each, 6 bales of hay at 60 lbs, tack etc. and your trailer now weighs about 3200+2200+360+100 = 5860 lbs. On the ball of the bumper pull hitch, this trailer would weigh about 580 lbs. To be safe, you would want to bump up to the next hitch class (only use weight distributing bumper pull hitches with sway control!), which would be 800 lbs.
Now, the same trailer may weigh 30% of the weight on the gooseneck ball (on your rear axle) - that would be anywhere between 1500 and 1800 lbs! To find the answer to your question of how much you can put on your rear axles, you can call Ford directly - they also publish a towing guide each year that lists all these numbers.
The best way to find out is to take your truck to the scales and weigh it with you and all other passengers and a full tank. You will get two numbers as a result - weight of your front axles (where the engine is) and weight of your rear axles (where you gooseneck hitch is). The front number will be much higher than the back number because of the weight of the engine.
Now, hook up the fully loaded trailer to it and go back to the scales (with your horses in it). Get both numbers again and compare the rear axle numbers before and after. The difference will be the weight of your trailer fully loaded on the rear axles of your truck. THIS will be the weight capacity your truck needs to satisfy to be safe on the rear axles.
This is my example: we have a 2015 3H 8ft LQ Exiss trailer. It weighs 12,500 lbs fully loaded with horses, generator, extra diesel and gas, hay for 10 days for two horses and all our camping gear. When I took it to the scales, it turned out it weighed 2600 lbs on the gooseneck hitch!!! We had a 2016 F-250 Powerstroke diesel at the time. It squatted that truck like it was nothing. The truck was at the border of its legal capacity of what can be put onto the rear axles (actually over it by a few hundred pounds). It needed a set of “super springs” in the back to level out the truck and stop it from squatting. Since there is only my wife and I riding in the truck (and Ford calculates 5 passengers in their weight calculations at 150 lbs each an my wife and I weigh combined 260 lbs), we “gained back” some load capacity by not having the three people in the back. However, technically we are overweight and should be moving into the dually category (which is the plan).
The 2016 F-250 diesel (I think) is rated to pull up to 14,500 lbs in the configuration we have (4x4, diesel, crew cab - all these add weight to the truck and take away from the towing capacity since 4x4 is heavy, diesel engine is much heavier that the gasser and crew cab weighs more than the basic two door cab). My trailer is within total towing capacity but NOT within what can go on the rear axles.
Most people would wave me off by saying that the 2016 F-250 diesel is more than capable of towing my trailer. And it is, in terms of diesel power (the F-350 dually has the same engine), braking capacity etc. etc. However, there is no knowing what long term consequences on the back axles and the frame are when towing extensively in this setup. I decided not to find out and just simply upgrade to the 2017 dually 
Hope the above helps!