I have two longcoat shepherds and have never had a problem with their hair catching. Now if the OWNER has long hair, I suggest pinning it up out of the way since you'll be leaning over your dog while you dremel. Fortunately, I did not have to learn this the hard way, someone else suggested it. I also use a dust mask since there is a lot of nail dust produced, and I have asthma.
I have caught my cat's hair - one time I was dremeling Cassidy's nails and Elvis came over to check out the treats I was giving her and I shoved him away.....with the hand holding the dremel, lol! Doh! It caught some of his tail hair, but he's a Maine **** and he has plenty of hair left.
When I do D & K's nails I pinch each nail between my fingers while I dremel, which stabilizes the nail and makes the grinding go much faster, plus it keeps the hair out of the way of the tool.
But if it's a concern, I've heard about the stocking trick too - I think Betty in MA, (who has 3 longcoats, including the famous Taser), does it that way. Her dogs have longer hair on their feet than mine do, and she trims it periodically, which I've never had to do.