The OP never said where his trailer was when his battery disappeared but if parked at home I'd be looking for somewhere else to live. :W During the season I keep our own trailer parked on our driveway, with the tongue enclosed with a fabric BBQ cover, primarily to protect the black plastic parts from fading, but I suppose it keeps the tongue components "out of sight, out of mind" - regardless, I've never had any issues in our neighbourhood with "sticky fingers". :B

While camping I've also never had any issues with
anything disappearing, don't take any special precautions other than storing my Weber Q out of sight when not in use, and frankly wouldn't ever give this any thought.
For winter storage I do strip the tongue of everything, mostly for cleaning up and preparing for the next season.
I guess that leaves parking the trailer in a remote storage lot between camping trips. Years ago when I did store in a remote lot during the season I never took any special precautions and also never had anything "disappear" but had I given it more thought I'd probably have secured the battery with the type of battery box lock linked to earlier and the propane tanks with a cable lock run through the tank collars and around the tongue.