Question
I live in southern in. Should I cut the vine back during the winter or leave the vines on the fence?

Answer
Hi Caroline,
Thanx for your question.  Any pruning or cutting back should be done in the late autumn.  Now would be fine.  There are basically three types of clematis and the type you have would depend on how much you prune it.  I generally, don't cut all the way back to the ground but instead, trim off dead or weak growth and make the vine neat.  Here's a link that I think will help you.  
Tom
http://www.aboutclematis.com/clematis_pruning.shtml