It's not always easy being a boss and running your own business is it? If you did not have to deal with people it would be a lot easier.
With the type of work he does, is this something your insurance company might have a say in? Are they likely to be faced with a reconstructive plastic surgery bill? There are plenty of jobs, usually around machinery or electricity, where you are not allowed to wear any jewelry, even wedding rings. Is there a safety hazard with him wearing that? But as Seed said, be consistent. Would dangling earrings constitute a safety hazard?
The rest relies on your judgement. As a business owner you are trying to present a certain climate for your customers. I'd think in your line of business you want your employees to look professional and competent, yet present a friendly helpful attitude. You might have a dress code, you might even provide uniforms. With the vet/boarding/grooming I use the employees wear jeans and tee shirts, not always highly stylish at all, they might even be stained. But it is somewhat a dirty job. I think they are dressed appropriately.
As the owner/boss you have the right to set that standard. You have a posh upscale clientele. How is that nose ring going to affect your business? Do you or others wear piercings at work? If you do I'm sure they are tasteful. Maybe he needs to tone it down a little. Would you be upset if he showed up with bright pink spiky hair? For all I know you do. How does that nose ring affect the face you want your business to present to the public?
Then you have the arbitrary "I'm the boss and I don't like it. Get rid of it!" You are paying the paycheck, they need to ride for the brand. I'm OK with that attitude, you are paying the paycheck. You just need to find employees that are OK with that. You attitude when you go about enforcing that can have a big effect on how well it works.
It's your call Boss.
A side story, nothing to do with appearance but a lot to do with the face you present to the public. As part of our move we will need to board our dogs for about a week and a half in that area. Yesterday my wife made some phone calls. One place she called the person that answered the phone did not have a good attitude. She was not happy with them at all. She knew how to handle that. Click! Another place did not return her phone call in a timely a manner. They did eventually return the call but it was several hours later. Too late. The third time was the charm. A helpful friendly attitude, they knew the relevant policies, and were willing to work with us. The rates are reasonable, even less than I pay here. A free grooming is included just before we pick them up. My wife checked them out online and they get high reviews. They also have a vet service so they may have found a couple of new clients. We'll make that evaluation when we get there but right now they are way ahead of their competitors.
. I don't remember doing that even when I worked at a greenhouse. Anyway, it was in a public place, seemed quite pleasant. There were other workers.
