In my experience, splints are most common in younger horses, but not limited to them. It's really no big deal. If the horse is lame, give them a few days off but if they aren't then you can continue to work them. My horse Denny started popping splints when he was somewhere around 6 and popped them several times over the next few years. Now, at 17, his front legs are hideous but he has never taken a lame step in his life.
From my understanding, they can be surgically removed but that is a procedure most often done on show horses where appearance is everything.