I would put a cover on the electrical plug, though. I don't have any experience with trailer electrics specifically, but I've spent way more than my share of time replacing connectors in a certain moto that will remain nameless. (Soldering is where I first realized I needed reading glasses...) Protecting exposed contacts is a good thing.
Speed comes from what you put behind you. - Judi Ketteler
Unless you got your hitch specifically to tow a trailer, you probably don't have plugs/wires. A bike rack hitch doesn't require it. But if it does - YES, cover those.
Mine doesn't have wires. And no, I don't use a cover.
Sarah
When it's easy, ride hard; when it's hard, ride easy.
2011 Volagi Liscio
2010 Pegoretti Love #3 "Manovelo"
2011 Mercian Vincitore Special
2003 Eddy Merckx Team SC - stolen
2001 Colnago Ovalmaster Stars and Stripes
Got Farm & Fleet over there? About $3 for a plastic one; but they're just cosmetic (covers the rusty scratched up hole).
Electra Townie 7D