Hi,
Snail vine will die back during cold snaps or frost. I found a link for desert tropicals that says to cut them back after frost hits them and they will come back in spring. Some people leave it and cut it back after frosts are through, but if there are any parts that are mushy I would cut them off now because they can cause fungal problems in the winter months.
Desert trops link seems to think that vigna caracalla (cork screw vine)and phalseolus caracalla (snail vine) are one and the same-a common mistake) snail vine has purple flowers that dont have a scent and corkscrew vine has purple and cream flowers that kinda twist around and hang and are imho wonderfully scented. corkscrew vine is a little more frost sensitive and has a tuber that you can dig up for the winter.
If you have the purple unscented snail vine you can just cut it back though.
~SJN

Here is a link that might be useful: snail vine

Thanks for your help Sultry Jasmine!!

Mine freeze every winter. I wait until early spring to cut them back to green stems and then they leaf out again! The dead leaves protect the plant during frosts, that's the reasoning for leaving them on all winter long...

Kevin

i ditto what kevin said. i have even given up on trying to cover them when we get a freeze warning because they still seem to get damaged no matter what i do.