I'm into my horses a little bit but I'm by no means an expert, but I was walking past a friends ground today that's more of a wooded & hilly area with lots of moss & brambles ect, where they used to keep some free range pigs but are now keeping their 2 ponies on it, a Shetland & section A or B cob, the ponies do have access to some but only small amounts of grass but get plenty of hay daily & used to be on our lowland grazing, until a few months ago.
Anyways the 1 thing I noticed were a few trees where the lower bark was stripped bare & also on a few fallen branches ( I don't know what type of trees.) But the only things I guess could have done it was the ponies, are they ok to eat this sort of stuff, I've heard that horses will do this occasionally if the grazing is poor.