The design will dictate the material strength required. Keep in mind one thing, with tubing you can have internal corrosion that go unseen until something fails. With C channel you can inspect everything from time to time to catch things before they become problems. I would guess that horse urine is corrosive to most materials. Calculating the strength required depends on the load and the bending moment of the beams used. The math is not difficult, and there are online calculators that make it simple and have libraries of common materials to plug the numbers in, for you. Horses are rather heavy and have small footprints, so you can consider them something of a point load rather than a distributed load. Also they can't be strapped down like other loads, so there will be a moment of inertia to contend with.
Long arc, short arc, heliarc and in-the-dark!