He wasn't specifically mentioned in any way, but some of his lines showed up on treebeards lips.

As for Sauron making an appearance during the third age, I think that in some ways he did. He rebuilt Barad-Dur early in the third age (and it took a long time). He also sent the great plague to depopulate Gondor, and he forced them to relax their vigilance by giving them some other things to worry about.

However, I think openly appearing as he did in the second age would be a bad idea until he had the armies to fight the free peoples of middle earth since if he did they would just destroy him again and then start worrying about him, perhaps uniting to destroy the evil men from the south so that Gondor could control Mordor without worrying about its borders. If he knew where the ring was he would use the ringwraiths to get it ASAP, but he didn't, so he trusted that eventually he could wear down Gondor enough to build an army.