The best way to keep an ice cube from melting is to use a cooler or another insulating container. You can also use a bag covered with a towel or other thick cloth to trap the cool temperature.
Putting cold water in the cooler can also slow the melting of ice. If you're using the ice to treat injuries, creating pykrete, which is ice mixed with paper pulp or wood shavings, makes the ice last significantly longer that pure ice alone. Aim for a concentration of approximately 17 percent pulp. Pykrete is also less prone to cracking and instead chips if it is dropped.