I use an open trailer and store my equipment in it seasonally. In the winter I store the equipment in a shed. While my trailer is parked with the equipment in it, it's in a carport. If I park it outside overnight, I have a heavy tarp I use leftover from my tractor trailer driving days.
The tow vehicle is the primary advertising tool, not the trailer. As mentioned, you won't get many calls from people seeing you driving around from an add on your truck (or trailer). The calls you do get, you might get one or two a year that actually hire you to perform work.
If you lived on a large property and could park an enclosed trailer with your company listed on it in a highly populated area, it might be worth while to invest in. Otherwise, I'd stick with an open trailer. There aren't many lawn equipment thefts where I am so theft is far from a concern.