Usually what they mean is that their horses are on grazing which looks something like the strip on the right hand side of the photo - incidentally, the photo is of a piece of our track where the horses can lean over and eat off the adjoining bank - its pretty obvious how far they can reach :-)
The grass on the left was mown 2 weeks ago, and had sheep on it before that but, with the current weather, its growing like crazy, of course.
So its worth realising that if you live in the UK and it looks as if your fields have "no grass" its probably not because you have your own special desert micro-climate. More likely, its because the grass has all been eaten by your horses and they haven't left much in the field :-)
At this time of year, a horse on a 1 acre starvation paddock getting "no grass", may in reality be eating 1 ft of grass x 1 acre every 2 weeks. Bear in mind that you would expect to cut 5-10 big bales of hay or haylage from the same area over 3 months, and that is actually quite a lot ;-)