Generally I agree with @beowulf beowulf and enjoy reading what she posts --but disagree today that hauling saddled is incredibly unsafe. With care and caution hauling saddled is as safe as any other type of hauling in “horse clothes” --coolers, leg wraps, shipping boots, blankets, fly masks, halters, etc. I have seen all of those catch or come loose or flap on horses being hauled.
I haul to every fox hunt saddled. I run up my stirrups and cover the saddle and stirrups with a padded saddle cover. My trailer does not have any pins or grommets that “stick out” that can catch on anything (seems like anything like that could catch on horse skin too). I saddle at home, and unload at the club, then lead my horse to the club barn. For me that makes much more sense than the activities of the other members who unload the horse, put him in a stall, bring saddle stands, brush boxes, saddles, bridles etc into the barn making multiple trips only to discover some important item has been left at home or in the trailer that is parked now at some distance.
Personally, over many years and miles of hauling, I have had shipping boots slide under hooves, leg wraps come undone, blankets slide off, halters catch on whatever, and tie ropes go every which way. I have yet to have an issue with a saddle. (Of course horses being horses, perhaps a matter of time)
I am comfortable hauling saddled. To me it makes sense.