See what I posted in this thread:
http://forum.barrowdowns.com/showthread.php?t=19149
The Dśnedain found the New Lands, but we have no evidence that they colonised them. However, as Arda is Earth, historically they were eventually.
The Easterlings always seemed more interested in conquering Western Middle-earth than anywhere else. Despite their allegiance to the technologically-minded Sauron, I also question whether they would have had the maritime resources or skill for the kind of seafaring accomplished by the Dśnedain. In any case, there's no information about it whatsoever as far as I know.