No - it does not get as cold down here as it does up there but when the temps are in the mid to upper 40's and the humidity is around 65% and you are riding at about 15 to 18 mph, it gets cold. At least to me, it does. That puts the wind chill at 38*F. I can't speak for you guys, but to me, that's cold - at best - very uncomfortable.
Having said that, I am also not into doing things that are boring, like cutting the grass. Enough of you here have emphasized the boredom factor enough to turn me off of the trainer.
Last winter, the things I had a problem with were fingers, feet, and face / ears. I guess I can go to full finger gloves, better socks, and as mentioned above, a ski mask. It will certainly be cheaper. Just had a funny thought - I'll probably get a few curious people when I go into a store to try on a face mask with a bike helmet.
Thanks to everyone for your great opinions and information. They have all helped a lot.