Fortunately, Caisson doesn't seem to mind, but I know what you mean! I had the same deal with Shadow .. I had put a real sheepskin cover on his girth. Now - he wore it for the entire ride with no problems, but when I unsaddled, I put the girth on the trailer fender. Oh Boy! Freakout time!
First time I tried the HorseDream pad on Caisson, I carefully asked him if it was OK, or if he thought it was going to eat him. Fortunately, he said it was OK. :)
Once Terri E. put the sheepskin pad on Reign, her mare & Reign told me in horse language that there was a dead kitten on her back & she couldn't possibly let Terri saddle her with that ! - Heidi