I seriously doubt many people, in this day and age, refer to the Civil War as the War of Northern Aggression or the War Between the States as the OP chooses to do so often, without making a serious mental effort to do so (at least until they have drilled it into their own brain). The folks who do use these alternate titles in an honest, sincere manner, as a result of upbringing and/or education, are extremely few and extremely far between.
To say that the modern day state of Texas and Texans are “Southern” in a general cultural sense is a VERY tough argument to make. Every bit as hard an argument as saying Oklahoma, Missouri, Kentucky, Florida and some would say West Virginia, Maryland and Delaware are “Southern”, again in a general cultural sense. These border states have some serious identity issues.
Texas pride and “Southern” pride aside I believe if one puts bias aside and objectively looks at the whole picture they couldn’t fail to come to the realization that the “Southerness” of the inhabitants of the aforementioned states (in general and including Texas) can only be determined on a case by case basis at best.
“Southern” culture, along with every other American subculture, is on its way to becoming a truly unfortunate casualty of the rise of the American macro culture, born of this melting pot which is a result of access to technology, urbanization, de-ruralization, emigration and immigration. There are few bastions of quintessential “Southern” culture left and Texas ain’t one of em. Neither are any of these other border states I mentioned earlier, including my own IMHO.
In short, not many Texans are actually “Southern”.
I realize your post was in jest so I apologize for any offense given.