The question shouldn't be "can an F350 pull it" it should be "can an F350 STOP it". I would go for the bigger trucks for a couple of reasons. First, you will destroy a regular pickup pulling this trailer very far. It's probably close to the max tow capacity before you load it with horses. Second, if the vehicle towing the trailer is too light you risk having the trailer push the truck down the hill. The bigger the truck the bigger the brakes and the more it weighs. Also it likely will have a heavier transmission and more gears. When you are pulling heavy loads gears are your friend.
There's nothing like the Rockies in the springtime... Nothing like the freedom in the air... And there ain't nothing better than draggin calves to the fire and there's nothing like the smell of burning hair. -Brenn Hill