We don't use a "chute" system, just specially designed corral area and Medina Hinge squeeze area along with a Swing Gate unit to encourage Longhorns into a trailer as needed.
As some "enlightment" for the non- and anti-Longhorn people, Longhorn Cattle are extremely clever, cautious, aware of the exact location of their horns and horn tips. Even one with 60 or 70 or 80" horns can negotiate a narrow place as "tight" as 2 to 3 feet wide. They will "thread" their horns through a variety of obstacles and situations, carefully and slowly...just let THEM analyze the situation and allow THEM to progress through the area. Obviously, if the wrangler tries to push, hoop & holler & shock them to go...well, a wreck is waiting to happen. The Longhorn has had over 500 years of genetics and learning on how to get into and out of tight situations. Give them a chance and don't rush them...they will figure it out on their own, safely, and without injuring themselves or anything/anyone else. Even when they are restrained in the Medina Hinge (2 heavy duty Priefert or similar gates), they will work their horns up or down the gate, one rail/one horn at a time until they get positioned where they want to be.