I'm not sure you are allowed to put your trailer on your site but I will admit I've seen it done. Besides, why take up the space.
I have a 7x10 Pace enclosed trailer for our golf cart ( actually it is for our Harleys ). When we get to FW we go directly to the overflow lot and unload the cart and then drop the trailer. I have a lock for the ball latch plus a lock the goes inside the the ball area, and last, I have a tire lock. This is similar to the boot locks that the NYPD use on cars with too many parking tickets. Also, you need a parking permit, from the Outpost, to leave a trailer in the lot.
We like to use the cart to check our site before I drive all the way there. After we get our site number and while I finish registration, DW will drive to our site in the cart and make sure the Coach will fit. Then she'll call me on the cell phone one way or the other.
There are some very expensive trailers, and boats, left in the overflow lot. I would think if there was an on going problem with theft, Disney would hear about it.