Wow, very interesting to read what everyone does. I've been wondering about this lately. I don't have a trailer, but have noticed that everyone I have trailered with seems to do it differently (they all have slant loads). My trainer ties through the window on the outside of the trailer (which I was told is actually a hazard; if the rope comes undone it could get caught in the wheel), another rider at the barn who I trailered with to a show doesn't tie the horses and ties the lead in a loop around their neck, and the last person I rode with unsnaps the lead and leaves them loose.
I asked my vet what the "correct" way to trailer a horse is and didn't really get an answer, just that a study showed that given the choice, most horses prefer to stand backwards at an angle while the trailer is moving. Tied or untied, this isn't an option for horses unless the trailer doesn't have dividers, or possibly in the last stall of a slant load.
This is one of those things where it seems like there should be a scientifically backed, "best" way to trailer horses, but the more I ask people about it, the more confused I get