If you have forgotten to plug up your stud holes either after your horse was shod or after your last event meaning they have become clogged with mud, stones and dirt the easiest time to clear them is after you have washed your horse. The water will have seeped up into the holes and will bind the mud allowing it to be removed in pieces more easily rather than scraping out dust.
When it comes to the cleaning process the best tool I have found is the humble farriers’ nail. I have a small collection donated by my farrier and they really can’t be beaten for getting the small bits out. Best of all your farrier will normally donate you a couple free if you ask.
If you are stuck with an annoying stone stuck in the stud hole then spray wd40 all round and underneath a jammed stone (use the straw thing they supply with the can), then trot the horse up and down on concrete. 9 times out if 10 the stone will have loosened and you will be able to pick it out without cutting and scraping your knuckles.