To me, it most certainly is and was a Southern state. Others opinions may differ. It is geographically beside Virginia and the culture was more closely related to the South.
How about Virginia being a Border State? She was a Border State according to one of Virginia's U.S. House members. (my bold) :
"We have heard southern statesmen dividing the South into 'cotton States' and
'border States.' Yea, even now, before we have made an effort at forming a southern confederacy, we observe this feeling manifesting itself. The Governor of South Carolina has recommended to his people that, under the new government of his State, she shall pass a law prohibiting the
border States from bringing their slaves into South Carolina. But if we should succeed in forming a southern confederacy, would not questions soon arise to disturb our harmony? The tariff, protection, direct tax, the African slave trade, would, I believe, become elements of discord.
"But, sir, evils greater than these present themselves to us. We of the
border States are very differently situated from our brethren of the 'cotton States.' We will be connected geographically with this hostile Republic, or Republics, for two thousand miles. We must suffer all the loss by escape of slave property, and bear the brunt and burden of all wars which must, in course of time, ensue. They would make common cause with us; but, from their geographical position and sparseness of white population, but few, comparatively, could leave their homes to fight in a distant country. Our States must be the battle-fields, and our border the scenes of blood and carnage. But, it may be said, there will be no war; that we can adjust all matters by treaty. If the North is so fanatical on the subject of slavery that we cannot live in a common Government with her, is it likely she would enter into a treaty by which fugitive slaves are to be returned? And if she did, would that treaty be any more respected than the fugitive slave bill is now?"
John Thomas Harris, of Virginia, before the House of Representatives, February 6, 1861