Suanne,
It depends on which kind of elephant ear it is. If it is the regular green elephant ear (Colocasia esculenta), the bulbs can be lifted and stored inside a dark closet/garage. Colocasia esculenta planted in the ground usually will overwinter fine in our zone, unless they stay overly wet and cold. I haven't overwintered any of these outside in containers, but would think that it needs to be kept on the dry side.

If your ear is another colocasia, overwintering care may be different. Some are more cold sensitive than others.