I'm pretty sure that they can but it is quite rare. As far as I'm aware it can sometimes go hand in hand with Cushing's, but the two are difficult to distinguish symptomatically. I'm no expert though so could be completely wrong!
There was a foal born somewhere in the USA this year who is thought to be the world's first truely diabetic horse. The owners were determined to do everything possible to try to help him, but I've not heard the outcome. Can't see it could possibly survive though in all honesty.