I had an Appy who scrambled mainly on left turns...not sure why, but no matter how slowly you entered or exited a left turn he would scramble slightly.
I made sure he was always adequately wrapped: if normal trailer wraps slide down his legs (they did on my App), use the thicker polos. I would rather have some protection than none. I also made sure to have those fleece halter protectors on the halter as well, so if he went down a bit, the halter didn't rub his face too badly. I also liked to have a light sheet on, to protect from scrapes from the divider...better the sheet than the horse. Most importantly I drove in such a way that he wasn't 'forced' to scramble as much; meaning I took longer to slow down, took a little longer to turn, etc...I could care less what other drivers think, my horse is WAY more important to me than getting somewhere in a hurry, they can pass me, or I will pull over and give people a chance to pass if I'm in an area that is hard for people TO pass easily.
I am fortunate, now, though, that my current mare is one of those that you don't even know she's there...haha. But I'm still careful with my precious cargo!
I tried both bedding and no bedding in the trailer, as well with the Appy, and neither seemed to make a difference, so I usually made sure he had a lot of bedding so IF by chance he ever did go down he didn't slide onto a hard floor; he never did go down which I am very thankful for.