I wouldn't do it, even if some company said that they could get it done. That is a big trailer, and when loaded up, I would bet that you are over the braking capacity of the truck, if not the payload. E.g.
(not picking on Chevy here)
A 2500 can trailer up to 16,500lbs, aka 3,300lbs on the truck via a gooseneck, which means that the truck needs to be close to empty as its capacity is only 3,794lbs, and empty that would leave you a net of 494lbs for you, your passengers and fuel. If you, your passengers, and your fuel weigh more than that, it cuts back into the trailer load capacity. (Fuel is going to be at least 260lbs full...)
Now let's take a stab at the trailer load; 4 Arabians at 1,000lbs a piece is 4,000lbs. A four horse slant load, with a 10' shortwall is going to be in the 8,000lb range, so that would be 12,000 before you have added tack, water, feed, etc. So at a minimum, the slide out, plus the engineering to strengthen the floor and walls wouldn't leave you with much of a remaining payload budget on either the truck or trailer.
I'm not saying that people don't grossly overload their trucks and trailers. People certainly do, and many get away with it. Location certainly matters; central Iowa has fewer challenges than upstate New York, or say Colorado or California. I'm just saying that there isn't a lot of elbow room to stay in the generally regarded as safe area.
You might look into a used toterhome, some of which are built to pull 70,000lbs easily. They often can be found at reasonable discounts to new because many are bought by car racing enthusiasts, depreciated, and then sold after five years.
All the best,
Peter