I've hauled sheep in a minivan and even one pony..That got a lot of looks when cars passed us and saw a horse looking morosely out at them

I had a horse delivered once in the back of a pickup with no rails but I personally wouldn't ever do it that way. It's possibly also against the law as in many places it's even against the law to have dogs untied in the back of trucks so they can't jump out.
Easy to get some pallets and bang them together to make stock racks that slide into the bed and latch together at the corners..you might want to make the inside solid faced at least at the bottom so nobody gets a foot caught in the spaces or tries to climb out. The back can be made up of a pallet or two with a solid top -3/4 in plywood is good with slats mounted on the face so they don't slip will carry a full size horse with no problem. I glued and nailed bits of old carpet under the slats..it gets messy sometimes but better that than an accident. This will act as a ramp that lifts up and becomes the back gate. Or, if you need something that will hold them in right away, make a sliding door that comes down as the last one goes in and use bolts that slide through to hold the ramp so it can be simply taken off and either left for another time or loaded on the side to unload at your destination.
Years ago nobody had trailers, they all used versions of stock racks if they had trucks. I have seen trailers made out of old truck boxes used to haul creatures as well..the sort of thing people make into utility trailers but with higher sides. It's now a sort of status thing to have trailers instead of stock racks I think.
I also moved an adult Arabian stallion 1500 or so miles in the back of a UHaul truck..I lined the sides and bottom with particle board, had LOTS of sawdust bedding and gated in the back with 2x6s then left the back door of the UHaul up. (Nothing was attached to the truck itself, it was a self contained thing, the back was kept from falling out by the way the truck box was built, I just had to make sure it wouldn't fall IN). People kept passing me and signalling that the back door was up

The first couple of times that happened I figured something was wrong but he travelled quite serenely. I was a bit concerned that the exhaust might curl up and into the truck box but it didn't seem to and it was a matter of no other options anyway. Even when we stopped overnight he was a happy camper. I didnt take him out but he had the equivilent of an 8x16 foot stall in there so figured he was ok for a day as long as he had water and hay. After taking out the panelling, all of which was resusable, and taking the truck through the carwash, the UHaul people never even knew what I had hauled in it.
