I had a horse in a trailering accident walk out unscathed in shipping boots and a bumper cap.
I always at least have brushing boots and bells on the horses' legs if I'm just driving the 3 miles to the x-country course. Longer trips I completely bandange and bell everything. If the horse is really a monkey or I'm worried I will put shipping boots over the bandages. Some horses prefer boots, some prefer bandages.
So were it me, I would have boots and bells on at least, if not shipping boots.
Good luck at the new barn and safe travels!
They say money doesn't buy happiness -- well happiness doesn't buy horses!