My son also enjoys nose-picking. And it started more like a nervous tic than a real "nose" issue too.
What I try to remember is that he is getting some kind of gratification from it. My job is to change this action into inconvenient work, and then to replace it with something positive that gives the same gratifying feeling his nostril treasure hunting is currently giving him.
So what we do is every time I see him picking his nose he has to stop what he's doing, go upstairs, wash his hands, wash whatever toy he's playing with (because now it has germs on it!), get a tissue, blow his nose, and throw away the tissue. He hates this routine. He can't stand leaving his play to do something so mundane. So I remind him how much easier it is to just get a tissue in the first place.
We're trying different things for replacement behavior. He likes to fiddle with his fingers in his nose, so we're trying to find other fiddly things for him to do. He's 5 yrs old, so coins in his pocket, or some small seashells, a small smooth stone, a jingle bell... anything for him to fiddle with. For a smaller child, maybe one of those little blankets with tags all over it. Or a scrap of textured fabric in his pocket. Or one of those squish balls (as long as it's too big to choke on.)
Just a couple ideas. Good luck!