We don't use a chute, no ours can't even think about getting through a regular chute. As far as loading in a cattle trailer, that's no big deal at all. We have six leases and we take corral panels and set them up out in the middle of the pasture, anywhere and load them right up when we need to. These cattle lead alot easier than they drive. Call them up with a bucket of range cubes and they'll follow you anywhere. Of course we don't pack them in real tight, don't want broken horns. But they really aren't any different than any other breed to handle, maybe a little easier to handle than some.
We have several 80" category horns on Longhorns. Also, quite a few in the 60-70" category. A Longhorn knows exactly where their tips are. Non-Longhorn people who have never seen one work their horns in/out/thru a variety of situations would be amazed at their agility. The Longhorn with carefully "thread" their rack through obstacles. They don't come crashing down/thru areas like some of the "wild" other breeds. The Longhorn evaluates the situation and then carefully negotiates their path. Even when in a "Medina Hinge" squeeze area a 60-80" animal can work it's way up and down the horizontal bars unless the gates are pressing too hard against their head or body.