All Confederates and all of their northern collaborators were Democrats. See http://www.republicanbasics.com and http://grandoldpartisan.typepad.com for more information.
I don't think it is quite true to say that all Confederates were Democrats. In 1860 the remnants of the Southern Whigs supported the Constitutional Union Party. After their own state seceded, many Southerners who had opposed secession still felt it was their duty to support their own state in the conflict. I imagine there must have been some Whigs among them.