The only thing that can melt ice (at normal pressures, anyway) is heat. All exhaled breath is warm (which is why we blow on our fingers to warm them up in cold weather) and if you were to blow long enough and hard enough onto some ice, it's surface would start to melt.
While the presence of bacteria (causing the halitosis) might just possibly increase the temperature of one's breath enough to register on an extremely accurate thermometer (capable of, say, detecting differences in temperature of one a hundredth of a degree Celsius), the very slightly higher temperature wouldn't be enough to make any noticeable difference in the rate that ice could be melted by one's breath.