Towing in an open trailer is the same as riding it on the road. It will get as dirty as it normally would except for maybe a little film from tow vehicle exhaust.
It won't be exposed to any more abuse than if you rode it the entire way.
I disagree based on my experience.
It will be much more exposed to whatever is on the road and get pelted by it and get much dirtier unless you are only towing on nice dry roads and never encounter any rain, construction, etc.. When you are riding the bike you are not riding six feet from the bumper of the vehicle in front of you. The tow vehicle will kick up all kinds of crap and coat the bike with it. Mud flaps prevent any larger heavier objects from becoming missiles but they don't stop the dirt laden water from being kicked up and blown backwards. Anyone who has followed behind a truck will have experienced this. It is not likely that it will result in any damage but it will make a mess on the bike.
One word of advice... do not use a cover! It will rub the finish right off your bike.
I agree, again based on my experience.
I made this mistake and wore the finish right off of the forks of my bike due to a flapping cover. It was well secured and tightly taped down to prevent flapping but it broke loose anyway. I had to have the forks re-chromed. If you absolutely want to cover it wrap it with a soft blanket first to protect it and then put the cover on securing it to eliminate any loose flapping material as much as possible. I did this on another trip and had no damage.
One thing that I have done when there is no protection in the front of the trailer that is cheap and simple to do and that works well, assuming that the bike is loaded facing forward, is I wrap the windshield, headlight and turn signals with cling wrap. You just have to peel it off when you get where you are going- much easier than trying to clean all of the grime off of them. If you will always be washing the bike when you arrive at your destination then this is not an issue of course.
You might consider making and installing a stone guard that attaches to the front of the trailer like is done for snowmobile trailers- sample picture below only to illustrate stone guard concept. It is much smaller and lighter than a fully enclosed trailer but still protects the towed vehicle. Where I lived in western Canada there were more gravel roads than paved roads. Everyone who towed a boat would make a stone guard out of plywood for the front of the trailer to protect the boat from the flying gravel. It woks quite well. You would only need something to deflect the air stream over the front of the bike so I am sure that you could make something similar out of plexiglass or something similar that is much lighter. There are also stone guards commercially available. With a little research you might be able to find one that will fit a small trailer. Here is an example-
Roadmaster Guardian Rock Guard.
