We have a few hundred metres of hawthorn in and around our garden and I reckon there are at least 8 different varieties in it. Some have large leaves, some have very small. Some are really thorny, some have no thorns on the new growth (hooray!) Some bits are completely covered in berries, some bits have no berries at all. Some have thorns at every leaf junction, some only have thorns more sporadically. My bunnies happily munch all of them - with a slight preference for the new growth, but they'll eat the whole lot.
If yours really love it, I would start collecting and drying it now, because the leaves will soon be dropping off - it looks like it should be evergreen but it isn't!