I'm pretty sure it would expand and go supernova before it collapsed and ' went out'. The first event would effectively roast most of the solar system, and the second would not have any witnesses.
Seriousness aside- the sun going out would probably be the ONLY way we'd get a REAL winter, and a white Christmas, in New Orleans.
I'd settle for it being moved just a bit farther out, but then nuclear winter sounds like a good thing to me! LOL
RE "I'm pretty sure it would expand and go supernova "
Expand yes. Supernova NO. Our sun is too small to fuse the heavy elements that are required to cause a supernova. I forget which elements bigger than helium can be fused by a star the size of our sun, but eventually it'll just burn out and be a dense cinder.