No, putting your head next to a pile of ice cubes would not enhance your hearing ability. While it is true that sound can be refracted or bent when passing through different mediums with varying temperatures, the effect of cold air on sound is generally negligible in everyday situations.
Sound waves are mechanical vibrations that travel through a medium, such as air. The speed of sound is influenced by factors like temperature, but the effect of temperature on sound propagation is relatively small unless extreme temperature differences exist. The refractive properties of air due to temperature variations are not significant enough to noticeably enhance your hearing ability.
Placing your head near a pile of ice cubes might make certain sounds slightly different due to the proximity of your ears to the source, or due to the vibrations being transmitted through the solid ice cubes, but this would not result in an actual improvement in your hearing acuity.