If an ice cube is stored in a freezer could it evaporate given enough time? Is there a temperature below which water cannot evaporate (even just a little)?
yes, this is called Sublimation.
Ice has a vapor pressure:
Molecules will go from the solid phase to the gas phase or visa versa depending upon whether the partial pressure of water vapor in the gas phase is above or below the vapor pressure of the ice, until equillibrium is reached.