I came across another fic today where Harry sees Snape's/Draco's arm with its Dark Mark and is shocked/disgusted/saddened/etc. by seeing it. And I was thinking that it doesn't really make much sense for it to be visible.
I've noticed that people who write fic like to have the Dark Mark visible on the arms of the Death Eaters/former Death Eaters all the time. But I'm not exactly sure about that... The only time we actually see or hear the Dark Mark and its visibility discussed in the books is in the Goblet of Fire when Karkaroff shows it to Snape and says "[i]t's been getting clearer" (ch. 23) and when Snape shows it to the Minister and says that it's "not as clear as it was ... when it burnt black, but you can still see it" (ch. 36). But doesn't "you can still see it" imply that we soon won't be able to anymore? If you think about it, it makes sense. Why would Voldemort have his followers branded with something that anybody could see if you'd just pull up their shirt sleeves?
During the First War people knew there were Death Eater spies everywhere. There was panic, people didn't know whom to trust. So if they could've recognised Death Eaters by their Mark, then they could just check their arms. The Ministry employees would have their arms checked every day before coming to work, and the trials would be made a bit more simple too (why would an Imperiused person have the Dark Mark?). Also, wouldn't it be simple to find the Death Eater spy in the Order if the Dark Mark was visible all the time and to anybody? Peter Pettigrew was branded by Voldemort, so all Dumbledore would have to do would be to check the arms of each Order member. The only reason why he wouldn't be able to do that was if the Dark Mark is not visible all the time.
Snape mentions that Voldemort had his followers branded so he'd be able to call them and so that they'd be able to distinguish each other. But this doesn't mean that anybody would be able to tell they're a Death Eater. Just the Death Eaters themselves. Of course that means that Snape could've found the spy in the Order... if he hadn't been spying for the Order at the time and had to keep it a secret.
Of course as Voldemort's resurrection became more imminent, the Dark Mark became visible. There didn't seem to be any need to keep it that hidden as everybody believed he was dead. It was probably also a really useful tactic to intimidate the Death Eaters and remind them that their master is coming back. But after the meeting at the graveyard, I imagine it faded again. They've seen Him, they know He's back, but they don't need anybody else to see their Marks by accident. Or, well, at least that's what I think. :)