There were German immigrants in the Hill Country of Texas in the mid-19th century (as in Luckenbach, Texas), also some in Arkansas (there is a Wiederkehr winery in western Arkansas). There were various other immigrant groups in Texas before the Civil War including Czechs and Wends (or Sorbs—Slavs from eastern Germany). There were some Croats in Louisiana. There were Irish in various places—there is a town called Erin in Tennessee reflecting that Irish presence.
You are right, of course. There was a famous massacre of Unionist Germans trying to get to Mexico so they could eventually join the Union Army.
http://en.wikipedia.org/wiki/Nueces_massacre
My point was that the huge majority of immigrants went to northern states, not that none went to the South.