Rick, the factory supplied rather than factory applied decals is probably the explanation why some of the archival photos have the donkey facing rearward and some forward. There is no "handedness" to text because the habit in the West is to read from left to right; "BURRO" on the driver's side must read from front to back and on the curb side back to front. It is possible to produce the donkey silouette either right or left-handed and I believe it was so done for the logos I have as the beast faces forward on both sides. Of course, if the logos were on separate contact sheets from the text, you could reverse the side applied to and both would then face rearward. It might seem that a foto transparency (possible that some archival pix came from the era of film cameras) could be flipped and a negative printed upside down which would change the direction of the donkey. However that would also reverse the image of the text and make it unreadable. So some jackasses are going with the flow and some headed back whence they came but it always says "BURRO".
It's likely that restorers of Burro trailers are getting replacement logos made by local graphics shops with CAD capability and CNC stylus machines. I know I did for both a spare tire cover and the front window gravel guard. If the owner has the residuum of an original logo to photograph and the overall size of original is noted the resulting replacement will likely be almost indistinguishable from the original except as to fidelity to the original "factory" colors.
Could it be that someone has applied a 3-D (molded) version of the braying beast to a trailer(s)? I'm also curious to see a foto of what Ed's talking about. If it's only the presence or absence of decals, no need to go further.