Thank you for your question. To my knowledge keeping ice under your chin will not benefit you at all. There is a new product available that permanently removes fat under the chin without surgery. It is called Kybella. It is an injection that devolves the fat under the chin. It typically takes two injection sessions are required. I recommend you check and see if you are a candidate. I hope you find this information useful.
Although I do not perform Coolsculpting in my practice, this device involves cooling of fat in problem areas with the idea that some of the fat will die and be "flushed out" of your system. In carefully selected patients, it may provide a modest non-surgical fat reduction. Liposuction is much more reliable and more effective. Use of an ice cube is more likely to cause harm than good.