I'd never leave them unattended tied to the trailer, I've seen them get cut, get their line caught (usually because it was too long) and more often than not in a bad scene, I've seen them break the welds on the trailer and bend things. Because it's risky, I am a little surprised it is your only option.
If I had to leave Bay tied to a trailer all night, I'd be sleeping right by him. I wouldn't want to be out of sight.
You are being judged in camp too and your camp setup and horse's camp manners are part of it. They want everone's horse's stabling conditions to be the same and they know that everyone at least has a trailer and a lead.