If you decide to park your trailer in the pasture, park it on a couple of sheets of plywood and remove your mats. The mats trap the moisture from the ground which speeds up rusting of the frame because the boards remain damp. The plywood prevents the grass from growing up around it which also holds moisture.
Saddlebag, that's really good advice. Also would keep the grass from growing up around or over the tongue, which is where I think the most danger is to the horse. If they get a foot caught in the open "v", they're more likely to cut a leg or hoof. The plywood would enable them to see the tongue at all times so they'd be less likely to run into it.