Tie baling twine around the metal hooks on trailer, and tie the horse to those via the lead rope. I would use a cotton lead rope.
A caveat learned the hard way - never use a nylon lead-rope or halter in a trailer. No nylon anything, not even nylon + breakway headstall. The reason I say this is because of Murphy’s Law - in trailer accidents, or mishaps, the horse never snags itself in a way where the breakway part of the halter can be utilized… my last time shipping in a nylon + breakway halter, the horse somehow got the nose part of the halter caught on the metal bar where the pin feeds through the butt-bar as he was backing up. You can imagine what happened - it was not pretty.
I do not use breakaway clips. They tend to 'bungi’e back under pressure/when they’re released, have had more than one horse whacked in the eye that way… which makes things worse.
I prefer to have the baling twine because it breaks before the horse goes into full panic mode, thus preventing that whole panic and get away from handler.
Each to their own - I find different disciplines have different expectations, and such.
You’ll see “hard-tie” thrown around as a term, it means the horse is tied to something unbreakable, with unbreakable material ( nylon). I have seen some serious accidents from hard tying and do not do it.
Teach the horse to yield to pressure and single-tie first. You can do this by teaching them to drop their head when you apply pressure, and walk forward when you pull on their halter. It wouldn’t hurt to teach them to ground-tie either.
I use an all leather halter, and cotton lead-ropes when tying to trailers.
The “Pony Club” way is to tie to a loop of baling twine that is around the trailer eye hook. Tie at heights that are at least the horse’s chest or above. I prefer eye (yours) level, but you can’t always control the height you tie to in a trailer. There should be minimal slack in the lead-rope, not enough for the horse to get a leg over, or walk away, but not so much that he can’t turn his neck (to nip at a fly on his chest, for instance).
I tie with an “emergency release” knot.
This shows what I mean by tying to baling twine:
https://www.youtube.com/watch?v=KIGDy7DNg7U
This is (more complicated) version of the knot I use:
https://www.youtube.com/watch?v=FyPwOgjPS70
Like this – but I would NEVER tie to a board of fence:
https://www.youtube.com/watch?v=ipOCj2WEhv0
I prefer those knots because in a panic you pull the end of the rope, and it’ll all come out, without part of the leadrope still being fed through whatever it is tied to.