Depends on the length of the trip, trailer and horse/s.
I usually haul in a stock trailer. In a stock trailer I almost always haul saddled. Depending on the length of haul, how many horses and which ones they may get hauled loose or tied. Unless it is an all day trip then turned out in a pen or stall, then unsaddled.
I have been in a hurry and hauled short distances bridled. Not my good bridles, but in snaffle rigs. If the reins or mecate is tied up properly, no danger.
Have to keep in mind it also depends on what your horses are used to. Mine are used to an open stock trailer saddled. If they get crammed in they get head and tailed. Or tied just like a slant load, or loose with just a couple of pasture mates...whatever...just depends.
I DON'T LEAD 'EM AND FEED 'EM, I RIDE 'EM AND SLIDE 'EM.