I think the shulchan aruch says that when going down to bath in the river he should cover his erva and when coming up to get dressed he shouldnt (I think) so people don't think he is embarassed of his bris.
In every mikveh I have ever been in everyone gets undressed and walks around and shmoozes, dries off. Yet I've come across a few guys that say you do need to be modest even in the mikva. Which is the right mhalech ? It seems it could be a bad thing to cover up either because it looks like you're embarased of your bris, or because you're essentially saying it's not right to be naked (like everyone there is doing).