The Elephant ear plants usually go dormant during the winter period. To take care of the plant, do not fertilize at all during the winter dormancy period. Keep your potted elephant ear plant in a cool, dry place during the winter when it has become dormant and its leaves have died back. Check out http://www.ehow.com/how_7171617_grow-elephant-ear-plants-indoors.html for more details.
No. It is a tropical annual and will not do well overwintering even if mulched and kept in a garage now of you want to bring it into your home and keep lightly fertilized over the winter, it might just make it. If you really like it, it's worth a try.