Great question. I have chosen not to use protection for transport, horses often loose it during transport, horses can move a lot because of it. My truck is really great so horses are very well protected, I think that protection can cause more troubles during transport.
For short distance (around and hour) trailer rides, I don’t tend to dress my horse in anything. For longer ones (long than an hour or two), I dress them in a cooler, shipping boots or standing wraps which are quilted pads held on with polo wraps. It’s up to you as well, if you know your horse would bang around much, you might not need much. However, you will still want to support their legs for longer journeys.