Some perfectly healty horses drag their hind feet when in soft terrain, like sand. If there's a health issue, such as a back injury or pelvic problem, terrain won't make much difference. Older horses with arthritis tend to start dragging the hind feet more with age and stiffness.
If your horse is sound and he doens't drag on real rocky ground or over obstacles, but does in the grass or arena, he's likely just being lazy. When he's frisky in the pasture, he'll pick them up more or if you are going at a faster pace.
Now, having said all that, shortening the toes for an injured horse would help some, but increases the likelyhood of overreaching (clipping the heels of his front feet). Anyways, most horses that drag their toes have already squared them off and trimming it more can create it's own problems.
A rolled toe is a bit different from a squared toe. Rolled, beveled, etc would apply to all of the hoof wall to some degree. If you truely square the toe, it makes it harder for the hoof to roll over to either side and could set the stage for a pastern injury and squared toes seem to crack more from the stress at the corners causing a shearing force. So if the bevel is increased, be sure the hoof still looks oval or round (matches the shape of the hoof at the hairline). Watch for overreaching and if the horse has already worn the hoof off in a square shape, the trimmer shouldn't shorten more, but just trim the hoof where it's not wearing to even out the wear.