You are going to have about 2,500 pounds to play with before being over your GVWR. Figure your empty truck at 8,000 pounds plus whatever you put in it including people. Typical GN puts 25% on the tongue so that would be a 10k loaded trailer. Otherwise, you will be up against your 20K GCVWR at a bit over 11K trailer weight. The 05 model year saw a massive increase in GVWR and GCVWR.
People are going to tell you it will pull whatever you hook up to it.
If you are going through mountains, I would be looking at a much larger truck for either trailer.
My rule of thumb is to add a 1 to the first number of the truck to determine the number of horses you can haul. That's just me though. I don't ever want to put ourselves or our horses in a bad spot when things go wrong.
Yes, do the math. It's not about how many horses it will haul or other people's stories -- it really is numbers and physics. A trailer's weight often can have nothing to do with its size either, but rather how it was built and material used. I am very leery of super-light trailers due to concerns about strength and engineering shortcuts. I'd rather pull a smaller, well-built trailer than a larger one that will turn into a tuna can in an accident.
Isn't the real question not what your truck can pull, but rather what can it stop? I've heard many stories of the trailer wagging the truck. I've also been told that a long wheel base on the truck makes a huge difference.
and which engine you have. The old 7.3 dielel we have, no problem. I hauled a steel 6 horse with 6 horses and a pony up over Jelico mountain and never knew it was back there.
My 2006 F350, crew cab, dually diesel with the "new motor" meh, you'd likely be fine with what you're thinking of hauling, I have a big 2+1 two BIG horses, no problem. 32 foot travel trailer, no problem. It does not pull weight as well as the 1999 with the 7.3. I love that truck. It's green, matches nothing but it pulls like a diesel train.
I think it would be ok with a loaded 6 horse with no living quarters, or maybe ok with, but, if where you plan to haul is uphill both ways you'll do it, but you will slow uphill.